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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 24, 'aut_gen_orders': [6, 4, 6, 6, 6, 6, 6], 'aut_gens': [[1, 2, 12, 72, 144, 864, 5184], [14401, 27370, 12684, 18648, 25200, 4320, 28512], [23261, 2767, 25816, 15552, 16344, 24912, 27432], [7641, 29162, 6708, 18216, 25632, 13104, 13464], [2549, 15002, 21252, 72, 4392, 17496, 23832], [30529, 23186, 12468, 72, 144, 864, 5184], [2017, 7274, 5124, 72, 144, 864, 5184], [29953, 19730, 18372, 72, 144, 864, 5184]], 'aut_group': '62208.eg', 'aut_hash': 8067873086317129283, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 62208, 'aut_permdeg': 99, 'aut_perms': [5292430173561415951474641372512982070966387451633531302517864379181244770650645860284802008435136490728385949023064709042945538020318845530510076394413103, 97078739529157482183300260422919544149654294345395800796007631983867059823488877640477635335271985981409373792932769591463440545181919109200233553074487328, 561008782196588483720317686524144886203675840865358109581791570016877099026787318013621709443002052872842913666546211516980307768111853752462462108410206540, 19269337041647922373847648465304644402200074483735900115749606512380666453640709509803633652348698074619922285157544129300951822398551449441195899569216180, 575358217691969591691521281258225154767701235188368082442480346306834423123342758647106959447312750088642751464937603610725834457281118767061085529903158584, 126244752854946434458869826909575289581935927305841126449218718736266524648745854192528170088881503574440365377927250292390452700834674851331171297955059407, 899559007154247630744207672345240401175197991546536795626941262496656780200946125519669982761701621132268942571907460814453309902618150213740146054409600689], 'aut_phi_ratio': 6.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 6, 1, 1], [2, 9, 1, 1], [2, 27, 1, 1], [2, 36, 2, 1], [2, 108, 1, 1], [2, 108, 2, 1], [2, 162, 1, 1], [2, 243, 1, 1], [2, 324, 1, 1], [3, 2, 2, 1], [3, 4, 1, 1], [3, 18, 1, 1], [3, 48, 1, 1], [3, 96, 1, 1], [3, 96, 2, 1], [3, 192, 2, 1], [3, 288, 1, 1], [3, 576, 2, 1], [4, 108, 1, 1], [4, 108, 2, 1], [4, 216, 1, 1], [4, 324, 1, 1], [4, 324, 2, 1], [4, 648, 1, 1], [6, 12, 1, 2], [6, 12, 2, 1], [6, 18, 1, 1], [6, 18, 2, 1], [6, 36, 1, 2], [6, 36, 2, 1], [6, 72, 1, 2], [6, 72, 2, 1], [6, 144, 1, 1], [6, 216, 2, 3], [6, 288, 1, 2], [6, 288, 2, 1], [6, 432, 1, 2], [6, 648, 1, 1], [6, 864, 2, 3], [6, 1296, 1, 1], [6, 1728, 2, 2], [12, 216, 2, 3], [12, 432, 1, 3], [12, 432, 2, 2], [12, 648, 1, 1], [12, 648, 2, 1], [12, 1296, 1, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3^2:S_4^2:D_6', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': '62208.eg', 'autcentquo_hash': 8067873086317129283, 'autcentquo_nilpotent': False, 'autcentquo_order': 62208, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^2:S_4^2:D_6', 'cc_stats': [[1, 1, 1], [2, 6, 1], [2, 9, 1], [2, 27, 1], [2, 36, 2], [2, 108, 3], [2, 162, 1], [2, 243, 1], [2, 324, 1], [3, 2, 2], [3, 4, 1], [3, 18, 1], [3, 48, 1], [3, 96, 3], [3, 192, 2], [3, 288, 1], [3, 576, 2], [4, 108, 3], [4, 216, 1], [4, 324, 3], [4, 648, 1], [6, 12, 4], [6, 18, 3], [6, 36, 4], [6, 72, 4], [6, 144, 1], [6, 216, 6], [6, 288, 4], [6, 432, 2], [6, 648, 1], [6, 864, 6], [6, 1296, 1], [6, 1728, 4], [12, 216, 6], [12, 432, 7], [12, 648, 3], [12, 1296, 1]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '31104.fx', 'commutator_count': 1, 'commutator_label': None, 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 12, 'conjugacy_classes_known': True, 'counter': 154, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 6, 1, 1], [2, 9, 1, 1], [2, 27, 1, 1], [2, 36, 1, 2], [2, 108, 1, 3], [2, 162, 1, 1], [2, 243, 1, 1], [2, 324, 1, 1], [3, 2, 1, 2], [3, 4, 1, 1], [3, 18, 1, 1], [3, 48, 1, 1], [3, 96, 1, 3], [3, 192, 1, 2], [3, 288, 1, 1], [3, 576, 1, 2], [4, 108, 1, 3], [4, 216, 1, 1], [4, 324, 1, 3], [4, 648, 1, 1], [6, 12, 1, 4], [6, 18, 1, 3], [6, 36, 1, 4], [6, 72, 1, 4], [6, 144, 1, 1], [6, 216, 1, 6], [6, 288, 1, 2], [6, 288, 2, 1], [6, 432, 1, 2], [6, 648, 1, 1], [6, 864, 1, 6], [6, 1296, 1, 1], [6, 1728, 1, 4], [12, 216, 1, 6], [12, 432, 1, 7], [12, 648, 1, 3], [12, 1296, 1, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 111041280, 'exponent': 12, 'exponents_of_order': [7, 5], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, 1, 2], [24, 0, 2], [24, 1, 2], [36, 1, 4], [72, 1, 1]], 'familial': False, 'frattini_label': '9.2', 'frattini_quotient': '3456.di', 'hash': 4394578261467941646, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 6, 6, 2, 6, 6, 6], 'inner_gens': [[1, 7810, 8268, 18216, 1584, 864, 25920], [26405, 2, 13308, 3096, 3960, 29736, 20808], [12985, 26090, 12, 18216, 5976, 30672, 29016], [18145, 3026, 18156, 72, 144, 864, 5184], [4609, 2378, 26292, 72, 144, 864, 5184], [1, 8426, 7356, 72, 144, 864, 5184], [10369, 15626, 13476, 72, 144, 864, 5184]], 'inner_hash': 4394578261467941646, 'inner_nilpotent': False, 'inner_order': 31104, 'inner_split': True, 'inner_tex': '(C_2^2\\times C_6^2).S_3^3', 'inner_used': [1, 2, 3], 'irrC_degree': 12, 'irrQ_degree': 12, 'irrQ_dim': 12, 'irrR_degree': 12, 'irrep_stats': [[1, 8], [2, 12], [4, 6], [6, 12], [8, 1], [9, 8], [12, 12], [18, 12], [24, 6], [36, 12], [72, 1]], 'label': '31104.fx', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': None, 'name': '(C2^2*C6^2).S3^3', 'ngens': 12, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 63, 'number_characteristic_subgroups': 19, 'number_conjugacy_classes': 90, 'number_divisions': 89, 'number_normal_subgroups': 51, 'number_subgroup_autclasses': 3388, 'number_subgroup_classes': 5307, 'number_subgroups': 616782, 'old_label': None, 'order': 31104, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 1167], [3, 2186], [4, 2160], [6, 18030], [12, 7560]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': True, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [0], 'outer_gens': [[29045, 25351, 9256, 72, 144, 17496, 25848]], 'outer_group': '2.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 2, 'outer_permdeg': 2, 'outer_perms': [1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2', 'pc_rank': 7, 'perfect': False, 'permutation_degree': 26, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 12], [4, 6], [6, 12], [8, 1], [9, 8], [12, 12], [18, 12], [24, 4], [36, 12], [48, 1], [72, 1]], 'representations': {'PC': {'code': '119890184407207179757406759844780055646911095066172618154088781912292380662955787528521834108248650523795478361967345166819252578493241306283346270246917834743121567423058618434746529690985261717457693307974804625990293', 'gens': [1, 2, 4, 6, 7, 9, 11], 'pres': [12, 2, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 3, 187441, 61, 2882, 396867, 319407, 185931, 135, 961924, 247696, 280108, 1311557, 111473, 327917, 109337, 54485, 133062, 166338, 241950, 41874, 20466, 246, 221191, 82963, 552991, 87595, 42679, 1605764, 649328, 276092, 134192, 320, 1382421, 328353, 241965, 112377, 3421450, 1373350, 786490, 319222, 131134, 394, 2985995, 248879]}, 'Perm': {'d': 26, 'gens': [17483017073855299676606627, 33637060727858918004567670, 49791356524424640277514966]}}, 'schur_multiplier': [2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 12, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': '(C_2^2\\times C_6^2).S_3^3', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}
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gps_conj_classes • Show schema
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id: 158102575
{'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 154, 'group_order': 31104, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
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id: 158102586
{'aut_label': '2A', 'centralizer': '6.f1', 'counter': 2, 'group_counter': 154, 'group_order': 31104, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 15552, 'size': 6}
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id: 158102597
{'aut_label': '2B', 'centralizer': '9.d1', 'counter': 3, 'group_counter': 154, 'group_order': 31104, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 432, 'size': 9}
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id: 158102608
{'aut_label': '2C', 'centralizer': '27.a1', 'counter': 4, 'group_counter': 154, 'group_order': 31104, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 23076, 'size': 27}
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id: 158102619
{'aut_label': '2D', 'centralizer': '36.di1', 'counter': 5, 'group_counter': 154, 'group_order': 31104, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 22479, 'size': 36}
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id: 158102630
{'aut_label': '2D', 'centralizer': '36.di1', 'counter': 6, 'group_counter': 154, 'group_order': 31104, 'label': '2E', 'order': 2, 'powers': [1, 6], 'representative': 22506, 'size': 36}
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id: 158102641
{'aut_label': '2F', 'centralizer': '108.gd1', 'counter': 7, 'group_counter': 154, 'group_order': 31104, 'label': '2F', 'order': 2, 'powers': [1, 7], 'representative': 14383, 'size': 108}
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id: 158102652
{'aut_label': '2F', 'centralizer': '108.gd1', 'counter': 8, 'group_counter': 154, 'group_order': 31104, 'label': '2G', 'order': 2, 'powers': [1, 8], 'representative': 18990, 'size': 108}
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id: 158102663
{'aut_label': '2H', 'centralizer': '108.d1', 'counter': 9, 'group_counter': 154, 'group_order': 31104, 'label': '2H', 'order': 2, 'powers': [1, 9], 'representative': 19501, 'size': 108}
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id: 158102576
{'aut_label': '2I', 'centralizer': '162.q1', 'counter': 10, 'group_counter': 154, 'group_order': 31104, 'label': '2I', 'order': 2, 'powers': [1, 10], 'representative': 27684, 'size': 162}
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id: 158102577
{'aut_label': '2J', 'centralizer': '243.a1', 'counter': 11, 'group_counter': 154, 'group_order': 31104, 'label': '2J', 'order': 2, 'powers': [1, 11], 'representative': 17388, 'size': 243}
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id: 158102578
{'aut_label': '2K', 'centralizer': '324.a1', 'counter': 12, 'group_counter': 154, 'group_order': 31104, 'label': '2K', 'order': 2, 'powers': [1, 12], 'representative': 28493, 'size': 324}
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id: 158102579
{'aut_label': '3A', 'centralizer': '2.c1', 'counter': 13, 'group_counter': 154, 'group_order': 31104, 'label': '3A', 'order': 3, 'powers': [13, 1], 'representative': 20736, 'size': 2}
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id: 158102580
{'aut_label': '3A', 'centralizer': '2.c1', 'counter': 14, 'group_counter': 154, 'group_order': 31104, 'label': '3B', 'order': 3, 'powers': [14, 1], 'representative': 22752, 'size': 2}
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id: 158102581
{'aut_label': '3C', 'centralizer': '4.d1', 'counter': 15, 'group_counter': 154, 'group_order': 31104, 'label': '3C', 'order': 3, 'powers': [15, 1], 'representative': 4032, 'size': 4}
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id: 158102582
{'aut_label': '3D', 'centralizer': '18.z1', 'counter': 16, 'group_counter': 154, 'group_order': 31104, 'label': '3D', 'order': 3, 'powers': [16, 1], 'representative': 288, 'size': 18}
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id: 158102583
{'aut_label': '3E', 'centralizer': '48.e1', 'counter': 17, 'group_counter': 154, 'group_order': 31104, 'label': '3E', 'order': 3, 'powers': [17, 1], 'representative': 15584, 'size': 48}
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id: 158102584
{'aut_label': '3F', 'centralizer': '96.o1', 'counter': 18, 'group_counter': 154, 'group_order': 31104, 'label': '3F', 'order': 3, 'powers': [18, 1], 'representative': 3072, 'size': 96}
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id: 158102585
{'aut_label': '3G', 'centralizer': '96.l1', 'counter': 19, 'group_counter': 154, 'group_order': 31104, 'label': '3G', 'order': 3, 'powers': [19, 1], 'representative': 13520, 'size': 96}
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id: 158102587
{'aut_label': '3F', 'centralizer': '96.o1', 'counter': 20, 'group_counter': 154, 'group_order': 31104, 'label': '3H', 'order': 3, 'powers': [20, 1], 'representative': 24344, 'size': 96}
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id: 158102588
{'aut_label': '3I', 'centralizer': '192.j1', 'counter': 21, 'group_counter': 154, 'group_order': 31104, 'label': '3I', 'order': 3, 'powers': [21, 1], 'representative': 19704, 'size': 192}
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id: 158102589
{'aut_label': '3I', 'centralizer': '192.j1', 'counter': 22, 'group_counter': 154, 'group_order': 31104, 'label': '3J', 'order': 3, 'powers': [22, 1], 'representative': 14404, 'size': 192}
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id: 158102590
{'aut_label': '3K', 'centralizer': '288.bm1', 'counter': 23, 'group_counter': 154, 'group_order': 31104, 'label': '3K', 'order': 3, 'powers': [23, 1], 'representative': 8624, 'size': 288}
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id: 158102591
{'aut_label': '3L', 'centralizer': '576.t1', 'counter': 24, 'group_counter': 154, 'group_order': 31104, 'label': '3L', 'order': 3, 'powers': [24, 1], 'representative': 25680, 'size': 576}
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id: 158102592
{'aut_label': '3L', 'centralizer': '576.t1', 'counter': 25, 'group_counter': 154, 'group_order': 31104, 'label': '3M', 'order': 3, 'powers': [25, 1], 'representative': 16780, 'size': 576}
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id: 158102593
{'aut_label': '4A', 'centralizer': '108.gh1', 'counter': 26, 'group_counter': 154, 'group_order': 31104, 'label': '4A', 'order': 4, 'powers': [3, 26], 'representative': 10002, 'size': 108}
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id: 158102594
{'aut_label': '4A', 'centralizer': '108.gh1', 'counter': 27, 'group_counter': 154, 'group_order': 31104, 'label': '4B', 'order': 4, 'powers': [3, 27], 'representative': 14559, 'size': 108}
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id: 158102595
{'aut_label': '4C', 'centralizer': '108.e1', 'counter': 28, 'group_counter': 154, 'group_order': 31104, 'label': '4C', 'order': 4, 'powers': [3, 28], 'representative': 425, 'size': 108}
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id: 158102596
{'aut_label': '4D', 'centralizer': '216.u1', 'counter': 29, 'group_counter': 154, 'group_order': 31104, 'label': '4D', 'order': 4, 'powers': [2, 29], 'representative': 10453, 'size': 216}
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id: 158102598
{'aut_label': '4E', 'centralizer': '324.em1', 'counter': 30, 'group_counter': 154, 'group_order': 31104, 'label': '4E', 'order': 4, 'powers': [3, 30], 'representative': 3702, 'size': 324}
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id: 158102599
{'aut_label': '4F', 'centralizer': '324.b1', 'counter': 31, 'group_counter': 154, 'group_order': 31104, 'label': '4F', 'order': 4, 'powers': [3, 31], 'representative': 97, 'size': 324}
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id: 158102600
{'aut_label': '4E', 'centralizer': '324.em1', 'counter': 32, 'group_counter': 154, 'group_order': 31104, 'label': '4G', 'order': 4, 'powers': [3, 32], 'representative': 26479, 'size': 324}
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id: 158102601
{'aut_label': '4H', 'centralizer': '648.w1', 'counter': 33, 'group_counter': 154, 'group_order': 31104, 'label': '4H', 'order': 4, 'powers': [2, 33], 'representative': 15537, 'size': 648}
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id: 158102602
{'aut_label': '6A', 'centralizer': '12.q1', 'counter': 34, 'group_counter': 154, 'group_order': 31104, 'label': '6A', 'order': 6, 'powers': [13, 2], 'representative': 13464, 'size': 12}
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id: 158102603
{'aut_label': '6B', 'centralizer': '12.q1', 'counter': 35, 'group_counter': 154, 'group_order': 31104, 'label': '6B', 'order': 6, 'powers': [15, 2], 'representative': 15480, 'size': 12}
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id: 158102604
{'aut_label': '6C', 'centralizer': '12.q1', 'counter': 36, 'group_counter': 154, 'group_order': 31104, 'label': '6C', 'order': 6, 'powers': [15, 2], 'representative': 20664, 'size': 12}
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id: 158102605
{'aut_label': '6A', 'centralizer': '12.q1', 'counter': 37, 'group_counter': 154, 'group_order': 31104, 'label': '6D', 'order': 6, 'powers': [14, 2], 'representative': 9864, 'size': 12}
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id: 158102606
{'aut_label': '6E', 'centralizer': '18.w1', 'counter': 38, 'group_counter': 154, 'group_order': 31104, 'label': '6E', 'order': 6, 'powers': [13, 3], 'representative': 25992, 'size': 18}
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id: 158102607
{'aut_label': '6F', 'centralizer': '18.z1', 'counter': 39, 'group_counter': 154, 'group_order': 31104, 'label': '6F', 'order': 6, 'powers': [16, 3], 'representative': 30672, 'size': 18}
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id: 158102609
{'aut_label': '6E', 'centralizer': '18.w1', 'counter': 40, 'group_counter': 154, 'group_order': 31104, 'label': '6G', 'order': 6, 'powers': [14, 3], 'representative': 14040, 'size': 18}
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id: 158102610
{'aut_label': '6H', 'centralizer': '36.cz1', 'counter': 41, 'group_counter': 154, 'group_order': 31104, 'label': '6H', 'order': 6, 'powers': [16, 2], 'representative': 18936, 'size': 36}
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id: 158102611
{'aut_label': '6I', 'centralizer': '36.bs1', 'counter': 42, 'group_counter': 154, 'group_order': 31104, 'label': '6I', 'order': 6, 'powers': [16, 3], 'representative': 10512, 'size': 36}
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id: 158102612
{'aut_label': '6I', 'centralizer': '36.bs1', 'counter': 43, 'group_counter': 154, 'group_order': 31104, 'label': '6J', 'order': 6, 'powers': [16, 3], 'representative': 9000, 'size': 36}
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id: 158102613
{'aut_label': '6K', 'centralizer': '36.cm1', 'counter': 44, 'group_counter': 154, 'group_order': 31104, 'label': '6K', 'order': 6, 'powers': [15, 3], 'representative': 5040, 'size': 36}
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id: 158102614
{'aut_label': '6L', 'centralizer': '72.a1', 'counter': 45, 'group_counter': 154, 'group_order': 31104, 'label': '6L', 'order': 6, 'powers': [16, 3], 'representative': 144, 'size': 72}
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id: 158102615
{'aut_label': '6M', 'centralizer': '72.a1', 'counter': 46, 'group_counter': 154, 'group_order': 31104, 'label': '6M', 'order': 6, 'powers': [16, 2], 'representative': 6912, 'size': 72}
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id: 158102616
{'aut_label': '6N', 'centralizer': '72.el1', 'counter': 47, 'group_counter': 154, 'group_order': 31104, 'label': '6N', 'order': 6, 'powers': [13, 5], 'representative': 1743, 'size': 72}
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id: 158102617
{'aut_label': '6N', 'centralizer': '72.el1', 'counter': 48, 'group_counter': 154, 'group_order': 31104, 'label': '6O', 'order': 6, 'powers': [14, 6], 'representative': 618, 'size': 72}
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id: 158102618
{'aut_label': '6P', 'centralizer': '144.bl1', 'counter': 49, 'group_counter': 154, 'group_order': 31104, 'label': '6P', 'order': 6, 'powers': [17, 2], 'representative': 52, 'size': 144}
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id: 158102620
{'aut_label': '6Q', 'centralizer': '216.ku1', 'counter': 50, 'group_counter': 154, 'group_order': 31104, 'label': '6Q', 'order': 6, 'powers': [13, 8], 'representative': 2022, 'size': 216}
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id: 158102621
{'aut_label': '6R', 'centralizer': '216.bb1', 'counter': 51, 'group_counter': 154, 'group_order': 31104, 'label': '6R', 'order': 6, 'powers': [14, 9], 'representative': 22309, 'size': 216}
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id: 158102622
{'aut_label': '6Q', 'centralizer': '216.ku1', 'counter': 52, 'group_counter': 154, 'group_order': 31104, 'label': '6S', 'order': 6, 'powers': [14, 7], 'representative': 15387, 'size': 216}
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id: 158102623
{'aut_label': '6T', 'centralizer': '216.le1', 'counter': 53, 'group_counter': 154, 'group_order': 31104, 'label': '6T', 'order': 6, 'powers': [16, 5], 'representative': 21835, 'size': 216}
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id: 158102624
{'aut_label': '6T', 'centralizer': '216.le1', 'counter': 54, 'group_counter': 154, 'group_order': 31104, 'label': '6U', 'order': 6, 'powers': [16, 6], 'representative': 2514, 'size': 216}
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id: 158102625
{'aut_label': '6R', 'centralizer': '216.bb1', 'counter': 55, 'group_counter': 154, 'group_order': 31104, 'label': '6V', 'order': 6, 'powers': [13, 9], 'representative': 7433, 'size': 216}
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id: 158102626
{'aut_label': '6W', 'centralizer': '288.bj1', 'counter': 56, 'group_counter': 154, 'group_order': 31104, 'label': '6W', 'order': 6, 'powers': [19, 2], 'representative': 5716, 'size': 288}
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id: 158102627
{'aut_label': '6X', 'centralizer': '288.bm1', 'counter': 57, 'group_counter': 154, 'group_order': 31104, 'label': '6X', 'order': 6, 'powers': [23, 2], 'representative': 26812, 'size': 288}
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id: 158102628
{'aut_label': '6Y1', 'centralizer': '288.bm1', 'counter': 58, 'group_counter': 154, 'group_order': 31104, 'label': '6Y1', 'order': 6, 'powers': [23, 2], 'representative': 11620, 'size': 288}
-
id: 158102629
{'aut_label': '6Y1', 'centralizer': '288.bm1', 'counter': 59, 'group_counter': 154, 'group_order': 31104, 'label': '6Y-1', 'order': 6, 'powers': [23, 2], 'representative': 21512, 'size': 288}
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id: 158102631
{'aut_label': '6Z', 'centralizer': '432.di1', 'counter': 60, 'group_counter': 154, 'group_order': 31104, 'label': '6Z', 'order': 6, 'powers': [15, 9], 'representative': 16333, 'size': 432}
-
id: 158102632
{'aut_label': '6AA', 'centralizer': '432.eq1', 'counter': 61, 'group_counter': 154, 'group_order': 31104, 'label': '6AA', 'order': 6, 'powers': [17, 4], 'representative': 2368, 'size': 432}
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id: 158102633
{'aut_label': '6AB', 'centralizer': '648.be1', 'counter': 62, 'group_counter': 154, 'group_order': 31104, 'label': '6AB', 'order': 6, 'powers': [16, 12], 'representative': 19565, 'size': 648}
-
id: 158102634
{'aut_label': '6AC', 'centralizer': '864.gp1', 'counter': 63, 'group_counter': 154, 'group_order': 31104, 'label': '6AC', 'order': 6, 'powers': [18, 7], 'representative': 22039, 'size': 864}
-
id: 158102635
{'aut_label': '6AC', 'centralizer': '864.gp1', 'counter': 64, 'group_counter': 154, 'group_order': 31104, 'label': '6AD', 'order': 6, 'powers': [20, 8], 'representative': 19570, 'size': 864}
-
id: 158102636
{'aut_label': '6AE', 'centralizer': '864.go1', 'counter': 65, 'group_counter': 154, 'group_order': 31104, 'label': '6AE', 'order': 6, 'powers': [18, 5], 'representative': 15743, 'size': 864}
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id: 158102637
{'aut_label': '6AF', 'centralizer': '864.gm1', 'counter': 66, 'group_counter': 154, 'group_order': 31104, 'label': '6AF', 'order': 6, 'powers': [20, 4], 'representative': 6160, 'size': 864}
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id: 158102638
{'aut_label': '6AF', 'centralizer': '864.gm1', 'counter': 67, 'group_counter': 154, 'group_order': 31104, 'label': '6AG', 'order': 6, 'powers': [18, 4], 'representative': 22596, 'size': 864}
-
id: 158102639
{'aut_label': '6AE', 'centralizer': '864.go1', 'counter': 68, 'group_counter': 154, 'group_order': 31104, 'label': '6AH', 'order': 6, 'powers': [20, 6], 'representative': 23566, 'size': 864}
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id: 158102640
{'aut_label': '6AI', 'centralizer': '1296.ei1', 'counter': 69, 'group_counter': 154, 'group_order': 31104, 'label': '6AI', 'order': 6, 'powers': [17, 10], 'representative': 30308, 'size': 1296}
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id: 158102642
{'aut_label': '6AJ', 'centralizer': '1728.bn1', 'counter': 70, 'group_counter': 154, 'group_order': 31104, 'label': '6AJ', 'order': 6, 'powers': [21, 7], 'representative': 14119, 'size': 1728}
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id: 158102643
{'aut_label': '6AK', 'centralizer': '1728.be1', 'counter': 71, 'group_counter': 154, 'group_order': 31104, 'label': '6AK', 'order': 6, 'powers': [24, 5], 'representative': 26903, 'size': 1728}
-
id: 158102644
{'aut_label': '6AJ', 'centralizer': '1728.bn1', 'counter': 72, 'group_counter': 154, 'group_order': 31104, 'label': '6AL', 'order': 6, 'powers': [22, 8], 'representative': 12098, 'size': 1728}
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id: 158102645
{'aut_label': '6AK', 'centralizer': '1728.be1', 'counter': 73, 'group_counter': 154, 'group_order': 31104, 'label': '6AM', 'order': 6, 'powers': [25, 6], 'representative': 12950, 'size': 1728}
-
id: 158102646
{'aut_label': '12A', 'centralizer': '216.lr1', 'counter': 74, 'group_counter': 154, 'group_order': 31104, 'label': '12A', 'order': 12, 'powers': [40, 26], 'representative': 27210, 'size': 216}
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id: 158102647
{'aut_label': '12B', 'centralizer': '216.lc1', 'counter': 75, 'group_counter': 154, 'group_order': 31104, 'label': '12B', 'order': 12, 'powers': [39, 27], 'representative': 1455, 'size': 216}
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id: 158102648
{'aut_label': '12C', 'centralizer': '216.bf1', 'counter': 76, 'group_counter': 154, 'group_order': 31104, 'label': '12C', 'order': 12, 'powers': [38, 28], 'representative': 26705, 'size': 216}
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id: 158102649
{'aut_label': '12A', 'centralizer': '216.lr1', 'counter': 77, 'group_counter': 154, 'group_order': 31104, 'label': '12D', 'order': 12, 'powers': [38, 27], 'representative': 17367, 'size': 216}
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id: 158102650
{'aut_label': '12C', 'centralizer': '216.bf1', 'counter': 78, 'group_counter': 154, 'group_order': 31104, 'label': '12E', 'order': 12, 'powers': [40, 28], 'representative': 11685, 'size': 216}
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id: 158102651
{'aut_label': '12B', 'centralizer': '216.lc1', 'counter': 79, 'group_counter': 154, 'group_order': 31104, 'label': '12F', 'order': 12, 'powers': [39, 26], 'representative': 15450, 'size': 216}
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id: 158102653
{'aut_label': '12G', 'centralizer': '432.ed1', 'counter': 80, 'group_counter': 154, 'group_order': 31104, 'label': '12G', 'order': 12, 'powers': [34, 29], 'representative': 3037, 'size': 432}
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id: 158102654
{'aut_label': '12H', 'centralizer': '432.ed1', 'counter': 81, 'group_counter': 154, 'group_order': 31104, 'label': '12H', 'order': 12, 'powers': [35, 29], 'representative': 1021, 'size': 432}
-
id: 158102655
{'aut_label': '12I', 'centralizer': '432.ed1', 'counter': 82, 'group_counter': 154, 'group_order': 31104, 'label': '12I', 'order': 12, 'powers': [36, 29], 'representative': 4649, 'size': 432}
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id: 158102656
{'aut_label': '12G', 'centralizer': '432.ed1', 'counter': 83, 'group_counter': 154, 'group_order': 31104, 'label': '12J', 'order': 12, 'powers': [37, 29], 'representative': 30641, 'size': 432}
-
id: 158102657
{'aut_label': '12K', 'centralizer': '432.ob1', 'counter': 84, 'group_counter': 154, 'group_order': 31104, 'label': '12K', 'order': 12, 'powers': [42, 26], 'representative': 23202, 'size': 432}
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id: 158102658
{'aut_label': '12K', 'centralizer': '432.ob1', 'counter': 85, 'group_counter': 154, 'group_order': 31104, 'label': '12L', 'order': 12, 'powers': [43, 27], 'representative': 2471, 'size': 432}
-
id: 158102659
{'aut_label': '12M', 'centralizer': '432.ec1', 'counter': 86, 'group_counter': 154, 'group_order': 31104, 'label': '12M', 'order': 12, 'powers': [44, 28], 'representative': 29349, 'size': 432}
-
id: 158102660
{'aut_label': '12N', 'centralizer': '648.iz1', 'counter': 87, 'group_counter': 154, 'group_order': 31104, 'label': '12N', 'order': 12, 'powers': [38, 30], 'representative': 8814, 'size': 648}
-
id: 158102661
{'aut_label': '12O', 'centralizer': '648.bf1', 'counter': 88, 'group_counter': 154, 'group_order': 31104, 'label': '12O', 'order': 12, 'powers': [39, 31], 'representative': 6577, 'size': 648}
-
id: 158102662
{'aut_label': '12N', 'centralizer': '648.iz1', 'counter': 89, 'group_counter': 154, 'group_order': 31104, 'label': '12P', 'order': 12, 'powers': [40, 32], 'representative': 20719, 'size': 648}
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id: 158102664
{'aut_label': '12Q', 'centralizer': '1296.ec1', 'counter': 90, 'group_counter': 154, 'group_order': 31104, 'label': '12Q', 'order': 12, 'powers': [41, 33], 'representative': 27705, 'size': 1296}
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gps_qchar • Show schema
Hide schema
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id: 15513957
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
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id: 15513968
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1], 'schur_index': 1}
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id: 15513979
{'cdim': 1, 'counter': 3, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, -1], 'schur_index': 1}
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id: 15513990
{'cdim': 1, 'counter': 4, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1], 'schur_index': 1}
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id: 15514001
{'cdim': 1, 'counter': 5, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.1e', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, -1, 1], 'schur_index': 1}
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id: 15514012
{'cdim': 1, 'counter': 6, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.1f', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1], 'schur_index': 1}
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id: 15514023
{'cdim': 1, 'counter': 7, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.1g', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1], 'schur_index': 1}
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id: 15514034
{'cdim': 1, 'counter': 8, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.1h', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1, 1, 1, -1, 1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, -1], 'schur_index': 1}
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id: 15514045
{'cdim': 2, 'counter': 9, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, -1, 2, 2, 2, 2, 2, 2, -1, -1, -1, 0, 2, 2, 0, 0, 2, 0, 2, 2, 2, 2, 2, 2, -1, 2, -1, -1, -1, 2, -1, -1, 2, 2, 2, 0, 0, -1, -1, 0, 0, -1, -1, 2, -1, 0, 0, -1, 2, 0, 2, 0, 0, 0, 0, 0, 0, -1, -1, 2, -1, 0, 2, 0, -1, 0, 0, -1, 0, 0, -1, 0, 0, -1, 0, -1], 'schur_index': 1}
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id: 15513958
{'cdim': 2, 'counter': 10, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.2b', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 2, 0, 2, 0, 2, 2, 0, 2, 2, 2, 2, -1, 2, -1, -1, 2, -1, -1, 2, -1, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, -1, 2, 0, 0, 2, 0, 0, -1, -1, -1, -1, 0, -1, 0, -1, 0, 0, -1, 2, -1, -1, 0, -1, -1, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0], 'schur_index': 1}
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id: 15513959
{'cdim': 2, 'counter': 11, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.2c', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, 2, -1, -1, -1, 2, -1, 2, -1, -1, 2, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, -1, 0, 0, 2, 0, 2, 0, -1, -1, -1, -1, 0, -1, 0, 0, -1, -1, 2, -1, 0, -1, -1, 0, 0, -1, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0], 'schur_index': 1}
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id: 15513960
{'cdim': 2, 'counter': 12, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.2d', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, -2, -2, 0, 2, 0, 0, -2, -2, 0, 2, 2, 2, 2, -1, -1, -1, 2, -1, 2, -1, -1, 2, 0, 0, -2, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, -2, -1, 0, 0, -2, 0, 2, 0, -1, -1, -1, -1, 0, 1, 0, 0, -1, 1, -2, 1, 0, 1, -1, 0, 0, 1, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0], 'schur_index': 1}
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id: 15513961
{'cdim': 2, 'counter': 13, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.2e', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, -2, 0, -2, 0, 2, 0, -2, -2, 0, 2, 2, 2, 2, -1, 2, -1, -1, 2, -1, -1, 2, -1, 0, -2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, 0, -1, 2, 0, 0, -2, 0, 0, -1, -1, -1, -1, 0, 1, 0, 1, 0, 0, 1, -2, -1, 1, 0, -1, 1, 0, -2, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0], 'schur_index': 1}
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id: 15513962
{'cdim': 2, 'counter': 14, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.2f', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, -2, 0, 2, 0, -2, 0, -2, -2, 0, 2, 2, 2, 2, -1, 2, -1, -1, 2, -1, -1, 2, -1, 0, 2, 0, 0, -2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, -1, -2, 0, 0, 2, 0, 0, -1, -1, -1, -1, 0, 1, 0, -1, 0, 0, 1, -2, 1, 1, 0, 1, -1, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0], 'schur_index': 1}
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id: 15513963
{'cdim': 2, 'counter': 15, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.2g', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, -2, 2, 0, -2, 0, 0, -2, -2, 0, 2, 2, 2, 2, -1, -1, -1, 2, -1, 2, -1, -1, 2, 0, 0, 2, 0, 0, 0, -2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, -1, 0, 0, 2, 0, -2, 0, -1, -1, -1, -1, 0, 1, 0, 0, 1, -1, -2, 1, 0, 1, 1, 0, 0, -1, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0], 'schur_index': 1}
-
id: 15513964
{'cdim': 2, 'counter': 16, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.2h', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 0, -2, -2, 0, 0, 0, 0, 0, 2, 2, 2, 2, -1, 2, 2, 2, 2, 2, 2, -1, -1, -1, 0, -2, -2, 0, 0, 2, 0, 2, 2, 2, 2, 2, 2, -1, 2, -1, -1, -1, 2, -1, -1, -2, -2, 2, 0, 0, 1, 1, 0, 0, -1, -1, 2, -1, 0, 0, -1, -2, 0, -2, 0, 0, 0, 0, 0, 0, 1, 1, -2, 1, 0, -2, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, -1, 0, -1], 'schur_index': 1}
-
id: 15513965
{'cdim': 2, 'counter': 17, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.2i', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 0, -2, 2, 0, 0, 0, 0, 0, -2, 2, 2, 2, -1, 2, 2, 2, 2, 2, 2, -1, -1, -1, 0, 2, -2, 0, 0, -2, 0, -2, 2, 2, 2, 2, 2, -1, 2, -1, -1, -1, 2, -1, -1, 2, -2, 2, 0, 0, 1, -1, 0, 0, -1, -1, 2, -1, 0, 0, 1, 2, 0, -2, 0, 0, 0, 0, 0, 0, -1, 1, 2, 1, 0, -2, 0, -1, 0, 0, -1, 0, 0, 1, 0, 0, 1, 0, 1], 'schur_index': 1}
-
id: 15513966
{'cdim': 2, 'counter': 18, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.2j', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 0, 2, -2, 0, 0, 0, 0, 0, -2, 2, 2, 2, -1, 2, 2, 2, 2, 2, 2, -1, -1, -1, 0, -2, 2, 0, 0, -2, 0, -2, 2, 2, 2, 2, 2, -1, 2, -1, -1, -1, 2, -1, -1, -2, 2, 2, 0, 0, -1, 1, 0, 0, -1, -1, 2, -1, 0, 0, 1, -2, 0, 2, 0, 0, 0, 0, 0, 0, 1, -1, -2, -1, 0, 2, 0, 1, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 1], 'schur_index': 1}
-
id: 15513967
{'cdim': 2, 'counter': 19, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.2k', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, 0, -2, 0, 0, 2, 2, 0, 2, 2, 2, 2, -1, -1, -1, 2, -1, 2, -1, -1, 2, 0, 0, -2, 0, 0, 0, -2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, -2, -1, 0, 0, -2, 0, -2, 0, -1, -1, -1, -1, 0, -1, 0, 0, 1, 1, 2, -1, 0, -1, 1, 0, 0, 1, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0], 'schur_index': 1}
-
id: 15513969
{'cdim': 2, 'counter': 20, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.2l', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, -2, 0, -2, 0, 2, 2, 0, 2, 2, 2, 2, -1, 2, -1, -1, 2, -1, -1, 2, -1, 0, -2, 0, 0, -2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, 0, -1, -2, 0, 0, -2, 0, 0, -1, -1, -1, -1, 0, -1, 0, 1, 0, 0, -1, 2, 1, -1, 0, 1, 1, 0, -2, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0], 'schur_index': 1}
-
id: 15513970
{'cdim': 4, 'counter': 21, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.4a', 'multiplicity': 1, 'nt': [6, 9], 'qdim': 4, 'qvalues': [4, 4, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 4, 4, -2, -2, 4, -2, -2, 4, -2, 1, -2, 1, 0, 4, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, -2, 4, -2, -2, -2, 4, -2, -2, 4, 0, -2, 0, 0, 0, -2, 0, 0, 1, 1, -2, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 4, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 15513971
{'cdim': 4, 'counter': 22, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.4b', 'multiplicity': 1, 'nt': [6, 9], 'qdim': 4, 'qvalues': [4, 4, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, -2, -2, -2, -2, 4, -2, 4, 1, 1, -2, 0, 0, 4, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, -2, 4, -2, -2, -2, 4, -2, -2, 0, 4, -2, 0, 0, -2, 0, 0, 0, 1, 1, -2, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, -2, 0, 4, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 15513972
{'cdim': 4, 'counter': 23, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.4c', 'multiplicity': 1, 'nt': [6, 9], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 1, -2, 1, -2, -2, -2, 1, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, -2, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 15513973
{'cdim': 4, 'counter': 24, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.4d', 'multiplicity': 1, 'nt': [12, 37], 'qdim': 4, 'qvalues': [4, 4, 4, -4, 0, 0, 0, 0, 0, -4, -4, 0, 4, 4, 4, 4, 1, -2, 1, -2, -2, -2, 1, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, -1, 0, 0, 0, 0, 2, 2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 15513974
{'cdim': 4, 'counter': 25, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.4e', 'multiplicity': 1, 'nt': [12, 37], 'qdim': 4, 'qvalues': [4, 4, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, -2, -2, -2, -2, 4, -2, 4, 1, 1, -2, 0, 0, -4, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, -2, 4, -2, -2, -2, 4, -2, -2, 0, -4, -2, 0, 0, 2, 0, 0, 0, 1, 1, -2, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 2, 0, -4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 15513975
{'cdim': 4, 'counter': 26, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.4f', 'multiplicity': 1, 'nt': [12, 37], 'qdim': 4, 'qvalues': [4, 4, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 4, 4, 4, -2, -2, 4, -2, -2, 4, -2, 1, -2, 1, 0, -4, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, -2, 4, -2, -2, -2, 4, -2, -2, -4, 0, -2, 0, 0, 0, 2, 0, 0, 1, 1, -2, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -4, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 15513976
{'cdim': 6, 'counter': 27, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.6a', 'multiplicity': 1, 'nt': [8, 45], 'qdim': 6, 'qvalues': [6, 2, -2, 6, 0, 0, 0, 0, 2, 2, -2, 2, 6, 6, 6, 6, 3, 0, 3, 0, 0, 0, 3, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 2, 2, 2, 2, -2, -2, -2, 2, -2, -2, -2, 2, -2, 0, 0, -1, 0, 2, 0, 0, 0, 2, -1, -1, -1, -1, 2, 3, 2, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0], 'schur_index': 1}
-
id: 15513977
{'cdim': 6, 'counter': 28, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.6b', 'multiplicity': 1, 'nt': [9, 18], 'qdim': 6, 'qvalues': [6, 6, 6, 0, 0, 6, 2, 0, 2, 0, 0, 0, 6, -3, -3, 0, 0, 6, 0, 0, -3, 0, 0, 0, 0, 2, 6, 0, 2, 0, 0, 2, 0, 6, -3, -3, -3, 6, 0, -3, 0, 0, 0, -3, 0, 0, -3, 0, 0, 0, -1, 0, 0, -1, 2, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, -3, 0, 2, 0, -1, 0, -1, -1, 0, 2, -1, 0, -1, 0, 0, -1, 0], 'schur_index': 1}
-
id: 15513978
{'cdim': 6, 'counter': 29, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.6c', 'multiplicity': 1, 'nt': [9, 18], 'qdim': 6, 'qvalues': [6, 6, 6, 0, 6, 0, 0, 2, 2, 0, 0, 0, -3, 6, -3, 0, 0, 0, 0, 6, 0, -3, 0, 0, 0, 2, 0, 6, 2, 2, 0, 0, 0, -3, -3, -3, 6, -3, 0, 6, 0, 0, 0, -3, 0, 0, 0, -3, 0, -1, 2, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -1, 0, 0, 0, 0, -1, -3, 2, 0, -1, -1, 0, -1, -1, 0, 2, -1, 0, 0, 0], 'schur_index': 1}
-
id: 15513980
{'cdim': 6, 'counter': 30, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.6d', 'multiplicity': 1, 'nt': [12, 161], 'qdim': 6, 'qvalues': [6, 2, -2, 6, 0, 0, 0, 0, -2, 2, -2, -2, 6, 6, 6, 6, 3, 0, 3, 0, 0, 0, 3, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 2, -2, -2, -2, 2, -2, -2, -2, 2, -2, 0, 0, -1, 0, -2, 0, 0, 0, -2, -1, -1, -1, -1, -2, 3, -2, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0], 'schur_index': 1}
-
id: 15513981
{'cdim': 6, 'counter': 31, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.6e', 'multiplicity': 1, 'nt': [12, 195], 'qdim': 6, 'qvalues': [6, 2, -2, -6, 0, 0, 0, 0, -2, -2, 2, 2, 6, 6, 6, 6, 3, 0, 3, 0, 0, 0, 3, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 2, 2, 2, 2, -2, -2, -2, 2, -2, -2, -2, 2, -2, 0, 0, -1, 0, -2, 0, 0, 0, -2, -1, -1, -1, -1, -2, -3, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0], 'schur_index': 1}
-
id: 15513982
{'cdim': 6, 'counter': 32, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.6f', 'multiplicity': 1, 'nt': [12, 195], 'qdim': 6, 'qvalues': [6, 2, -2, -6, 0, 0, 0, 0, 2, -2, 2, -2, 6, 6, 6, 6, 3, 0, 3, 0, 0, 0, 3, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 2, -2, -2, -2, 2, -2, -2, -2, 2, -2, 0, 0, -1, 0, 2, 0, 0, 0, 2, -1, -1, -1, -1, 2, -3, -2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0], 'schur_index': 1}
-
id: 15513983
{'cdim': 6, 'counter': 33, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.6g', 'multiplicity': 1, 'nt': [18, 51], 'qdim': 6, 'qvalues': [6, 6, 6, 0, 0, 6, -2, 0, -2, 0, 0, 0, 6, -3, -3, 0, 0, 6, 0, 0, -3, 0, 0, 0, 0, -2, 6, 0, -2, 0, 0, -2, 0, 6, -3, -3, -3, 6, 0, -3, 0, 0, 0, -3, 0, 0, -3, 0, 0, 0, 1, 0, 0, 1, -2, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, -3, 0, -2, 0, 1, 0, 1, 1, 0, -2, 1, 0, 1, 0, 0, 1, 0], 'schur_index': 1}
-
id: 15513984
{'cdim': 6, 'counter': 34, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.6h', 'multiplicity': 1, 'nt': [18, 51], 'qdim': 6, 'qvalues': [6, 6, 6, 0, 6, 0, 0, -2, -2, 0, 0, 0, -3, 6, -3, 0, 0, 0, 0, 6, 0, -3, 0, 0, 0, -2, 0, 6, -2, -2, 0, 0, 0, -3, -3, -3, 6, -3, 0, 6, 0, 0, 0, -3, 0, 0, 0, -3, 0, 1, -2, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, 1, -3, -2, 0, 1, 1, 0, 1, 1, 0, -2, 1, 0, 0, 0], 'schur_index': 1}
-
id: 15513985
{'cdim': 6, 'counter': 35, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.6i', 'multiplicity': 1, 'nt': [18, 94], 'qdim': 6, 'qvalues': [6, 6, 6, 0, -6, 0, 0, -2, 2, 0, 0, 0, -3, 6, -3, 0, 0, 0, 0, 6, 0, -3, 0, 0, 0, 2, 0, -6, 2, -2, 0, 0, 0, -3, -3, -3, 6, -3, 0, 6, 0, 0, 0, -3, 0, 0, 0, 3, 0, 1, 2, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, -1, 3, 2, 0, -1, -1, 0, -1, -1, 0, 2, 1, 0, 0, 0], 'schur_index': 1}
-
id: 15513986
{'cdim': 6, 'counter': 36, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.6j', 'multiplicity': 1, 'nt': [18, 94], 'qdim': 6, 'qvalues': [6, 6, 6, 0, -6, 0, 0, 2, -2, 0, 0, 0, -3, 6, -3, 0, 0, 0, 0, 6, 0, -3, 0, 0, 0, -2, 0, -6, -2, 2, 0, 0, 0, -3, -3, -3, 6, -3, 0, 6, 0, 0, 0, -3, 0, 0, 0, 3, 0, -1, -2, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -1, 0, 0, 0, 0, 1, 3, -2, 0, 1, 1, 0, 1, 1, 0, -2, -1, 0, 0, 0], 'schur_index': 1}
-
id: 15513987
{'cdim': 6, 'counter': 37, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.6k', 'multiplicity': 1, 'nt': [18, 94], 'qdim': 6, 'qvalues': [6, 6, 6, 0, 0, -6, -2, 0, 2, 0, 0, 0, 6, -3, -3, 0, 0, 6, 0, 0, -3, 0, 0, 0, 0, 2, -6, 0, 2, 0, 0, -2, 0, 6, -3, -3, -3, 6, 0, -3, 0, 0, 0, -3, 0, 0, 3, 0, 0, 0, -1, 0, 0, 1, 2, 0, 0, 0, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 3, 0, 2, 0, -1, 0, -1, -1, 0, 2, -1, 0, -1, 0, 0, 1, 0], 'schur_index': 1}
-
id: 15513988
{'cdim': 6, 'counter': 38, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.6l', 'multiplicity': 1, 'nt': [18, 94], 'qdim': 6, 'qvalues': [6, 6, 6, 0, 0, -6, 2, 0, -2, 0, 0, 0, 6, -3, -3, 0, 0, 6, 0, 0, -3, 0, 0, 0, 0, -2, -6, 0, -2, 0, 0, 2, 0, 6, -3, -3, -3, 6, 0, -3, 0, 0, 0, -3, 0, 0, 3, 0, 0, 0, 1, 0, 0, -1, -2, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 3, 0, -2, 0, 1, 0, 1, 1, 0, -2, 1, 0, 1, 0, 0, -1, 0], 'schur_index': 1}
-
id: 15513989
{'cdim': 8, 'counter': 39, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.8a', 'multiplicity': 1, 'nt': [12, 117], 'qdim': 8, 'qvalues': [8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, -4, 2, -4, 2, -4, -4, -4, -1, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, -4, 8, -4, -4, -4, 8, -4, -4, 0, 0, 2, 0, 0, 0, 0, 0, 0, -1, -1, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 15513991
{'cdim': 9, 'counter': 40, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.9a', 'multiplicity': 1, 'nt': [12, 165], 'qdim': 9, 'qvalues': [9, -3, 1, 9, 3, 3, 3, 3, 1, -3, 1, 1, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, -1, -1, 1, -1, -1, -3, -3, -3, -3, 1, 1, 1, -3, 1, 1, 1, -3, 1, 3, 3, 0, 3, 1, 3, 3, 3, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1], 'schur_index': 1}
-
id: 15513992
{'cdim': 9, 'counter': 41, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.9b', 'multiplicity': 1, 'nt': [18, 179], 'qdim': 9, 'qvalues': [9, -3, 1, 9, -3, -3, -3, -3, 1, -3, 1, 1, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, -1, 1, 1, 1, -1, -3, -3, -3, -3, 1, 1, 1, -3, 1, 1, 1, -3, 1, -3, -3, 0, -3, 1, -3, -3, -3, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1], 'schur_index': 1}
-
id: 15513993
{'cdim': 9, 'counter': 42, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.9c', 'multiplicity': 1, 'nt': [18, 185], 'qdim': 9, 'qvalues': [9, -3, 1, 9, -3, 3, -3, 3, -1, -3, 1, -1, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 1, 1, -1, -1, 1, 1, -3, -3, -3, -3, 1, 1, 1, -3, 1, 1, 1, -3, 1, 3, -3, 0, 3, -1, -3, 3, -3, -1, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, -1, 1, -1, -1, 1, 1, -1, 1, -1, 1, 1, -1, -1, 1, 1], 'schur_index': 1}
-
id: 15513994
{'cdim': 9, 'counter': 43, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.9d', 'multiplicity': 1, 'nt': [18, 185], 'qdim': 9, 'qvalues': [9, -3, 1, 9, 3, -3, 3, -3, -1, -3, 1, -1, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, -1, 1, 1, -1, -1, 1, -3, -3, -3, -3, 1, 1, 1, -3, 1, 1, 1, -3, 1, -3, 3, 0, -3, -1, 3, -3, 3, -1, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1], 'schur_index': 1}
-
id: 15513995
{'cdim': 9, 'counter': 44, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.9e', 'multiplicity': 1, 'nt': [18, 267], 'qdim': 9, 'qvalues': [9, -3, 1, -9, -3, -3, 3, 3, -1, 3, -1, 1, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 1, 1, -1, 1, -1, -1, -3, -3, -3, -3, 1, 1, 1, -3, 1, 1, 1, -3, 1, -3, -3, 0, 3, -1, -3, -3, 3, -1, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1], 'schur_index': 1}
-
id: 15513996
{'cdim': 9, 'counter': 45, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.9f', 'multiplicity': 1, 'nt': [18, 267], 'qdim': 9, 'qvalues': [9, -3, 1, -9, -3, 3, 3, -3, 1, 3, -1, -1, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 1, -1, 1, -1, -1, 1, -3, -3, -3, -3, 1, 1, 1, -3, 1, 1, 1, -3, 1, 3, -3, 0, -3, 1, -3, 3, 3, 1, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, -1, -1, 1], 'schur_index': 1}
-
id: 15513997
{'cdim': 9, 'counter': 46, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.9g', 'multiplicity': 1, 'nt': [18, 267], 'qdim': 9, 'qvalues': [9, -3, 1, -9, 3, -3, -3, 3, 1, 3, -1, -1, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1, -1, -1, -1, 1, 1, -3, -3, -3, -3, 1, 1, 1, -3, 1, 1, 1, -3, 1, -3, 3, 0, 3, 1, 3, -3, -3, 1, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 1, -1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1], 'schur_index': 1}
-
id: 15513998
{'cdim': 9, 'counter': 47, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.9h', 'multiplicity': 1, 'nt': [18, 267], 'qdim': 9, 'qvalues': [9, -3, 1, -9, 3, 3, -3, -3, -1, 3, -1, 1, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 1, 1, 1, 1, -1, -3, -3, -3, -3, 1, 1, 1, -3, 1, 1, 1, -3, 1, 3, 3, 0, -3, -1, 3, 3, -3, -1, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, -1, -1, 1, 1, 1, 1, -1], 'schur_index': 1}
-
id: 15513999
{'cdim': 12, 'counter': 48, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.12a', 'multiplicity': 1, 'nt': [18, 191], 'qdim': 12, 'qvalues': [12, 12, 12, 0, 0, 0, 0, 4, 0, 0, 0, 0, -6, 12, -6, 0, 0, 0, 0, -6, 0, 3, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -6, -6, -6, 12, -6, 0, 12, 0, 0, 0, -6, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0], 'schur_index': 1}
-
id: 15514000
{'cdim': 12, 'counter': 49, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.12b', 'multiplicity': 1, 'nt': [18, 191], 'qdim': 12, 'qvalues': [12, 12, 12, 0, 0, 0, 4, 0, 0, 0, 0, 0, 12, -6, -6, 0, 0, -6, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 12, -6, -6, -6, 12, 0, -6, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0], 'schur_index': 1}
-
id: 15514002
{'cdim': 12, 'counter': 50, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.12c', 'multiplicity': 1, 'nt': [18, 342], 'qdim': 12, 'qvalues': [12, 12, 12, 0, 0, 0, 0, 0, 4, 0, 0, 0, -6, -6, 3, 0, 6, 0, -3, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, -6, 3, 3, -6, -6, 0, -6, 0, 0, 0, 3, 0, 0, 0, 0, 6, 0, -2, 0, 0, 0, -2, 0, 0, -3, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 1, 1, 0, -2, 1, 0, -2, 0, 0, 0, 0], 'schur_index': 1}
-
id: 15514003
{'cdim': 12, 'counter': 51, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.12d', 'multiplicity': 1, 'nt': [24, 1503], 'qdim': 12, 'qvalues': [12, 4, -4, 12, 0, 0, 0, 0, 0, 4, -4, 0, 12, 12, 12, 12, -3, 0, -3, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, -4, -4, -4, 4, -4, -4, -4, 4, -4, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, -3, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 15514004
{'cdim': 12, 'counter': 52, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.12e', 'multiplicity': 1, 'nt': [24, 7230], 'qdim': 12, 'qvalues': [12, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 12, 12, 12, -6, 6, 0, 6, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 4, 4, 4, 4, -4, 2, -4, -2, 2, 2, -4, -2, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 1, 1, -2, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0], 'schur_index': 1}
-
id: 15514005
{'cdim': 12, 'counter': 53, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.12f', 'multiplicity': 1, 'nt': [36, 1084], 'qdim': 12, 'qvalues': [12, 12, 12, 0, 0, 0, -4, 0, 0, 0, 0, 0, 12, -6, -6, 0, 0, -6, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 12, -6, -6, -6, 12, 0, -6, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0], 'schur_index': 1}
-
id: 15514006
{'cdim': 12, 'counter': 54, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.12g', 'multiplicity': 1, 'nt': [36, 1084], 'qdim': 12, 'qvalues': [12, 12, 12, 0, 0, 0, 0, -4, 0, 0, 0, 0, -6, 12, -6, 0, 0, 0, 0, -6, 0, 3, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -6, -6, -6, 12, -6, 0, 12, 0, 0, 0, -6, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0], 'schur_index': 1}
-
id: 15514007
{'cdim': 12, 'counter': 55, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.12h', 'multiplicity': 1, 'nt': [36, 1655], 'qdim': 12, 'qvalues': [12, 4, -4, -12, 0, 0, 0, 0, 0, -4, 4, 0, 12, 12, 12, 12, -3, 0, -3, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, -4, -4, -4, 4, -4, -4, -4, 4, -4, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 3, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 15514008
{'cdim': 12, 'counter': 56, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.12i', 'multiplicity': 1, 'nt': [36, 2757], 'qdim': 12, 'qvalues': [12, 12, 12, 0, 0, 0, 0, 0, -4, 0, 0, 0, -6, -6, 3, 0, 6, 0, -3, 0, 0, 0, 0, 0, 0, -4, 0, 0, -4, 0, 0, 0, 0, -6, 3, 3, -6, -6, 0, -6, 0, 0, 0, 3, 0, 0, 0, 0, 6, 0, 2, 0, 0, 0, 2, 0, 0, -3, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, -1, -1, 0, 2, -1, 0, 2, 0, 0, 0, 0], 'schur_index': 1}
-
id: 15514009
{'cdim': 12, 'counter': 57, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.12j', 'multiplicity': 1, 'nt': [36, 4392], 'qdim': 12, 'qvalues': [12, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 12, 12, 12, -6, 6, 0, 6, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 4, 4, -4, 2, -4, -2, 2, 2, -4, -2, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 1, 1, -2, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0], 'schur_index': 1}
-
id: 15514010
{'cdim': 12, 'counter': 58, 'faithful': True, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.12k', 'multiplicity': 1, 'nt': [36, 13453], 'qdim': 12, 'qvalues': [12, 4, -4, 0, 0, 0, 0, 0, 4, 0, 0, 0, -6, -6, 3, 0, 6, 0, -3, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -2, -5, 7, -2, 2, 8, 2, 4, -4, -4, -1, -2, 2, 0, 0, -2, 0, -2, 0, 0, 0, -2, 4, -2, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 3, -3, 0, 0, -1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 15514011
{'cdim': 12, 'counter': 59, 'faithful': True, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.12l', 'multiplicity': 1, 'nt': [36, 13455], 'qdim': 12, 'qvalues': [12, 4, -4, 0, 0, 0, 0, 0, -4, 0, 0, 0, -6, -6, 3, 0, 6, 0, -3, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -2, -5, 7, -2, 2, 8, 2, 4, -4, -4, -1, -2, 2, 0, 0, -2, 0, 2, 0, 0, 0, 2, 4, -2, 1, -2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, -3, 3, 0, 0, 1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 15514013
{'cdim': 18, 'counter': 60, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.18a', 'multiplicity': 1, 'nt': [36, 4545], 'qdim': 18, 'qvalues': [18, -6, 2, 0, 6, 6, 0, 0, 0, 0, 0, 2, 18, 18, 18, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 2, 0, -2, -6, -6, -6, -6, 2, -1, 2, 3, -1, -1, 2, 3, -1, 6, 6, 0, 0, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 0, -2, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, -1, 0, 1], 'schur_index': 1}
-
id: 15514014
{'cdim': 18, 'counter': 61, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.18b', 'multiplicity': 1, 'nt': [36, 9018], 'qdim': 18, 'qvalues': [18, -6, 2, 0, 0, 6, 6, 0, 2, 0, 0, 0, 18, -9, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, -2, 0, 0, -2, 0, -6, 3, 3, 3, 2, 8, -1, 0, -4, 8, -1, 0, -4, -3, 0, 0, 0, -1, 0, 0, -3, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, -1, 4, 1, 1, -2, -2, -1, 0, 1, 0, 0, 1, 0], 'schur_index': 1}
-
id: 15514015
{'cdim': 18, 'counter': 62, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.18c', 'multiplicity': 1, 'nt': [36, 9018], 'qdim': 18, 'qvalues': [18, -6, 2, 0, 6, 0, 0, 6, 2, 0, 0, 0, -9, 18, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, -2, -2, 0, 0, 0, 3, 3, 3, -6, -1, 8, 2, 0, 8, -4, -1, 0, -4, 0, -3, 0, -3, 2, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -1, 1, 2, 0, 1, 1, 0, 1, -1, -2, -2, 1, 0, 0, 0], 'schur_index': 1}
-
id: 15514016
{'cdim': 18, 'counter': 63, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.18d', 'multiplicity': 1, 'nt': [54, 0], 'qdim': 18, 'qvalues': [18, -6, 2, 0, -6, -6, 0, 0, 0, 0, 0, 2, 18, 18, 18, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, -2, -6, -6, -6, -6, 2, -1, 2, 3, -1, -1, 2, 3, -1, -6, -6, 0, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, 0, 2, 0, -1, 0, 0, -1, 0, 0, -1, 0, 0, -1, 0, 1], 'schur_index': 1}
-
id: 15514017
{'cdim': 18, 'counter': 64, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.18e', 'multiplicity': 1, 'nt': [54, 0], 'qdim': 18, 'qvalues': [18, -6, 2, 0, -6, 0, 0, -6, 2, 0, 0, 0, -9, 18, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, -2, 2, 0, 0, 0, 3, 3, 3, -6, -1, 8, 2, 0, 8, -4, -1, 0, -4, 0, 3, 0, 3, 2, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -1, -1, 2, 0, 1, 1, 0, 1, -1, 2, -2, -1, 0, 0, 0], 'schur_index': 1}
-
id: 15514018
{'cdim': 18, 'counter': 65, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.18f', 'multiplicity': 1, 'nt': [54, 0], 'qdim': 18, 'qvalues': [18, -6, 2, 0, -6, 0, 0, 6, -2, 0, 0, 0, -9, 18, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 2, -2, 0, 0, 0, 3, 3, 3, -6, -1, 8, 2, 0, 8, -4, -1, 0, -4, 0, 3, 0, -3, -2, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 1, -1, -2, 0, -1, -1, 0, -1, 1, 2, 2, 1, 0, 0, 0], 'schur_index': 1}
-
id: 15514019
{'cdim': 18, 'counter': 66, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.18g', 'multiplicity': 1, 'nt': [54, 0], 'qdim': 18, 'qvalues': [18, -6, 2, 0, -6, 6, 0, 0, 0, 0, 0, -2, 18, 18, 18, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, -2, 0, 2, -6, -6, -6, -6, 2, -1, 2, 3, -1, -1, 2, 3, -1, 6, -6, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -1, 0, 2, 0, 1, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, -1], 'schur_index': 1}
-
id: 15514020
{'cdim': 18, 'counter': 67, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.18h', 'multiplicity': 1, 'nt': [54, 0], 'qdim': 18, 'qvalues': [18, -6, 2, 0, 0, -6, -6, 0, 2, 0, 0, 0, 18, -9, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, -2, 0, 0, 2, 0, -6, 3, 3, 3, 2, 8, -1, 0, -4, 8, -1, 0, -4, 3, 0, 0, 0, -1, 0, 0, 3, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 2, 0, -1, -4, 1, 1, 2, -2, -1, 0, 1, 0, 0, -1, 0], 'schur_index': 1}
-
id: 15514021
{'cdim': 18, 'counter': 68, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.18i', 'multiplicity': 1, 'nt': [54, 0], 'qdim': 18, 'qvalues': [18, -6, 2, 0, 0, -6, 6, 0, -2, 0, 0, 0, 18, -9, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 2, 0, 0, -2, 0, -6, 3, 3, 3, 2, 8, -1, 0, -4, 8, -1, 0, -4, 3, 0, 0, 0, 1, 0, 0, -3, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -2, 0, 1, -4, -1, -1, 2, 2, 1, 0, -1, 0, 0, 1, 0], 'schur_index': 1}
-
id: 15514022
{'cdim': 18, 'counter': 69, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.18j', 'multiplicity': 1, 'nt': [54, 0], 'qdim': 18, 'qvalues': [18, -6, 2, 0, 0, 6, -6, 0, -2, 0, 0, 0, 18, -9, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 2, 0, 0, 2, 0, -6, 3, 3, 3, 2, 8, -1, 0, -4, 8, -1, 0, -4, -3, 0, 0, 0, 1, 0, 0, 3, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -2, 0, 1, 4, -1, -1, -2, 2, 1, 0, -1, 0, 0, -1, 0], 'schur_index': 1}
-
id: 15514024
{'cdim': 18, 'counter': 70, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.18k', 'multiplicity': 1, 'nt': [54, 0], 'qdim': 18, 'qvalues': [18, -6, 2, 0, 6, -6, 0, 0, 0, 0, 0, -2, 18, 18, 18, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, -2, 0, 2, -6, -6, -6, -6, 2, -1, 2, 3, -1, -1, 2, 3, -1, -6, 6, 0, 0, 0, -3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, -2, 0, -1, 0, 0, -1, 0, 0, 1, 0, 0, 1, 0, -1], 'schur_index': 1}
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id: 15514025
{'cdim': 18, 'counter': 71, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.18l', 'multiplicity': 1, 'nt': [54, 0], 'qdim': 18, 'qvalues': [18, -6, 2, 0, 6, 0, 0, -6, -2, 0, 0, 0, -9, 18, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 2, 2, 0, 0, 0, 3, 3, 3, -6, -1, 8, 2, 0, 8, -4, -1, 0, -4, 0, -3, 0, 3, -2, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 1, 1, -2, 0, -1, -1, 0, -1, 1, -2, 2, -1, 0, 0, 0], 'schur_index': 1}
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id: 15514026
{'cdim': 24, 'counter': 72, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.24a', 'multiplicity': 1, 'nt': [36, 2819], 'qdim': 24, 'qvalues': [24, 24, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, -12, 6, 0, -6, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 6, 6, -12, -12, 0, -12, 0, 0, 0, 6, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 15514027
{'cdim': 24, 'counter': 73, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.24b', 'multiplicity': 1, 'nt': [48, 0], 'qdim': 24, 'qvalues': [24, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 24, 24, -12, -6, 0, -6, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, -8, 4, -8, -4, 4, 4, -8, -4, 4, 0, 0, 2, 0, 0, 0, 0, 0, 0, -1, -1, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 15514028
{'cdim': 24, 'counter': 74, 'faithful': True, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.24c', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, -12, 6, 0, -6, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -10, 14, -4, 4, 16, 4, 8, -8, -8, -2, -4, 4, 0, 0, 2, 0, 0, 0, 0, 0, 0, -4, 2, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 15514029
{'cdim': 24, 'counter': 75, 'faithful': True, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.24d', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, -12, 6, 0, 12, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -10, 14, -4, 4, -8, 4, -4, 4, 4, -2, 2, -2, 0, 0, -4, 0, 0, 0, 0, 0, 0, -4, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 15514031
{'cdim': 36, 'counter': 77, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.36a', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 36, 'qvalues': [36, -12, 4, 0, 0, 12, 0, 0, 0, 0, 0, 0, 36, -18, -18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, -12, 6, 6, 6, 4, -8, -2, 0, 4, -8, -2, 0, 4, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -4, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 15514032
{'cdim': 36, 'counter': 78, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.36b', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 36, 'qvalues': [36, -12, 4, 0, 12, 0, 0, 0, 0, 0, 0, 0, -18, 36, -18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 6, 6, 6, -12, -2, -8, 4, 0, -8, 4, -2, 0, 4, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 15514033
{'cdim': 36, 'counter': 79, 'faithful': True, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.36c', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 36, 'qvalues': [36, 12, -12, 0, 0, 0, 0, 0, 4, 0, 0, 0, -18, -18, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -6, 21, -15, -6, 6, 0, 6, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, -3, 3, 0, 0, -1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 15514035
{'cdim': 36, 'counter': 80, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.36d', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 36, 'qvalues': [36, 12, -12, 0, 0, 0, 0, 0, 4, 0, 0, 0, -18, 36, -18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -6, -6, -6, 12, 6, 0, -12, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 15514036
{'cdim': 36, 'counter': 81, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.36e', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 36, 'qvalues': [36, 12, -12, 0, 0, 0, 0, 0, 4, 0, 0, 0, 36, -18, -18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 12, -6, -6, -6, -12, 0, 6, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 4, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 15514037
{'cdim': 36, 'counter': 82, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.36f', 'multiplicity': 1, 'nt': [108, 0], 'qdim': 36, 'qvalues': [36, -12, 4, 0, -12, 0, 0, 0, 0, 0, 0, 0, -18, 36, -18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 6, 6, 6, -12, -2, -8, 4, 0, -8, 4, -2, 0, 4, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 15514038
{'cdim': 36, 'counter': 83, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.36g', 'multiplicity': 1, 'nt': [108, 0], 'qdim': 36, 'qvalues': [36, -12, 4, 0, 0, -12, 0, 0, 0, 0, 0, 0, 36, -18, -18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -12, 6, 6, 6, 4, -8, -2, 0, 4, -8, -2, 0, 4, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 4, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 15514039
{'cdim': 36, 'counter': 84, 'faithful': True, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.36h', 'multiplicity': 1, 'nt': [108, 0], 'qdim': 36, 'qvalues': [36, -12, 4, 0, 0, 0, 0, 0, -4, 0, 0, 0, -18, -18, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 4, 0, 0, 0, 0, 6, -3, -3, 6, -2, -8, -2, 12, 4, 4, 1, -6, -2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 1, 1, 0, -2, -1, 0, -2, 0, 0, 0, 0], 'schur_index': 1}
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id: 15514040
{'cdim': 36, 'counter': 85, 'faithful': True, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.36i', 'multiplicity': 1, 'nt': [108, 0], 'qdim': 36, 'qvalues': [36, -12, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, -18, -18, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -4, 0, 0, 0, 0, 6, -3, -3, 6, -2, -8, -2, 12, 4, 4, 1, -6, -2, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, -1, -1, 0, 2, 1, 0, 2, 0, 0, 0, 0], 'schur_index': 1}
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id: 15514041
{'cdim': 36, 'counter': 86, 'faithful': True, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.36j', 'multiplicity': 1, 'nt': [108, 0], 'qdim': 36, 'qvalues': [36, 12, -12, 0, 0, 0, 0, 0, -4, 0, 0, 0, -18, -18, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -6, 21, -15, -6, 6, 0, 6, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 3, -3, 0, 0, 1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 15514042
{'cdim': 36, 'counter': 87, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.36k', 'multiplicity': 1, 'nt': [108, 0], 'qdim': 36, 'qvalues': [36, 12, -12, 0, 0, 0, 0, 0, -4, 0, 0, 0, -18, 36, -18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -6, -6, -6, 12, 6, 0, -12, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 15514043
{'cdim': 36, 'counter': 88, 'faithful': False, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.36l', 'multiplicity': 1, 'nt': [108, 0], 'qdim': 36, 'qvalues': [36, 12, -12, 0, 0, 0, 0, 0, -4, 0, 0, 0, 36, -18, -18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 12, -6, -6, -6, -12, 0, 6, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 15514030
{'cdim': 24, 'counter': 76, 'faithful': True, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.24e', 'multiplicity': 2, 'nt': [144, 0], 'qdim': 48, 'qvalues': [48, 16, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, -24, 12, 0, -12, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, -20, 28, -8, 8, -16, 8, -8, 8, 8, -4, 4, -4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 15514044
{'cdim': 72, 'counter': 89, 'faithful': True, 'group': '31104.fx', 'group_order': 31104, 'image': None, 'label': '31104.fx.72a', 'multiplicity': 1, 'nt': [216, 0], 'qdim': 72, 'qvalues': [72, -24, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -36, -36, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, -6, -6, 12, -4, 8, -4, -12, -4, -4, 2, 6, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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gps_char • Show schema
Hide schema
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id: 35404139
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id: 35404150
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id: 35404161
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id: 35404172
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id: 35404183
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id: 35404194
{'center': '1.a1', 'center_index': 1, 'center_order': 31104, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 15552, 'label': '31104.fx.1f', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
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id: 35404205
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id: 35404216
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id: 35404227
{'center': '6.b1', 'center_index': 6, 'center_order': 5184, 'counter': 9, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.b1', 'kernel_order': 5184, 'label': '31104.fx.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]]]}
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id: 35404140
{'center': '6.a1', 'center_index': 6, 'center_order': 5184, 'counter': 10, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1', 'kernel_order': 5184, 'label': '31104.fx.2b', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35404141
{'center': '6.a1', 'center_index': 6, 'center_order': 5184, 'counter': 11, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1', 'kernel_order': 5184, 'label': '31104.fx.2c', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]]]}
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id: 35404142
{'center': '6.a1', 'center_index': 6, 'center_order': 5184, 'counter': 12, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.d1', 'kernel_order': 2592, 'label': '31104.fx.2d', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]]]}
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id: 35404143
{'center': '6.a1', 'center_index': 6, 'center_order': 5184, 'counter': 13, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.d1', 'kernel_order': 2592, 'label': '31104.fx.2e', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35404144
{'center': '6.a1', 'center_index': 6, 'center_order': 5184, 'counter': 14, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.b1', 'kernel_order': 2592, 'label': '31104.fx.2f', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35404145
{'center': '6.a1', 'center_index': 6, 'center_order': 5184, 'counter': 15, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.b1', 'kernel_order': 2592, 'label': '31104.fx.2g', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]]]}
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id: 35404146
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id: 35404147
{'center': '6.b1', 'center_index': 6, 'center_order': 5184, 'counter': 17, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.c1', 'kernel_order': 2592, 'label': '31104.fx.2i', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]]]}
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id: 35404148
{'center': '6.b1', 'center_index': 6, 'center_order': 5184, 'counter': 18, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.c1', 'kernel_order': 2592, 'label': '31104.fx.2j', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]]]}
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id: 35404149
{'center': '6.a1', 'center_index': 6, 'center_order': 5184, 'counter': 19, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1', 'kernel_order': 2592, 'label': '31104.fx.2k', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]]]}
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id: 35404151
{'center': '6.a1', 'center_index': 6, 'center_order': 5184, 'counter': 20, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1', 'kernel_order': 2592, 'label': '31104.fx.2l', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35404152
{'center': '36.b1', 'center_index': 36, 'center_order': 864, 'counter': 21, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '36.10', 'image_order': 36, 'indicator': 1, 'kernel': '36.b1', 'kernel_order': 864, 'label': '31104.fx.4a', 'nt': [6, 9], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35404153
{'center': '36.b1', 'center_index': 36, 'center_order': 864, 'counter': 22, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '36.10', 'image_order': 36, 'indicator': 1, 'kernel': '36.b1', 'kernel_order': 864, 'label': '31104.fx.4b', 'nt': [6, 9], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35404154
{'center': '36.a1', 'center_index': 36, 'center_order': 864, 'counter': 23, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '36.10', 'image_order': 36, 'indicator': 1, 'kernel': '36.a1', 'kernel_order': 864, 'label': '31104.fx.4c', 'nt': [6, 9], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35404155
{'center': '36.a1', 'center_index': 36, 'center_order': 864, 'counter': 24, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '72.46', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1', 'kernel_order': 432, 'label': '31104.fx.4d', 'nt': [12, 37], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35404156
{'center': '36.b1', 'center_index': 36, 'center_order': 864, 'counter': 25, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '72.46', 'image_order': 72, 'indicator': 1, 'kernel': '72.b1', 'kernel_order': 432, 'label': '31104.fx.4e', 'nt': [12, 37], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35404157
{'center': '36.b1', 'center_index': 36, 'center_order': 864, 'counter': 26, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '72.46', 'image_order': 72, 'indicator': 1, 'kernel': '72.b1', 'kernel_order': 432, 'label': '31104.fx.4f', 'nt': [12, 37], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35404158
{'center': '576.a1', 'center_index': 576, 'center_order': 54, 'counter': 27, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '576.8654', 'image_order': 576, 'indicator': 1, 'kernel': '576.a1', 'kernel_order': 54, 'label': '31104.fx.6a', 'nt': [8, 45], 'q_character': None, 'values': [[[6, 0]], [[2, 0]], [[-2, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[3, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]]]}
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id: 35404159
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id: 35404160
{'center': '108.a1', 'center_index': 108, 'center_order': 288, 'counter': 29, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '108.17', 'image_order': 108, 'indicator': 1, 'kernel': '108.a1', 'kernel_order': 288, 'label': '31104.fx.6c', 'nt': [9, 18], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[6, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-3, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35404162
{'center': '576.a1', 'center_index': 576, 'center_order': 54, 'counter': 30, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '576.8654', 'image_order': 576, 'indicator': 1, 'kernel': '576.a1', 'kernel_order': 54, 'label': '31104.fx.6d', 'nt': [12, 161], 'q_character': None, 'values': [[[6, 0]], [[2, 0]], [[-2, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[3, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]]]}
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id: 35404163
{'center': '576.a1', 'center_index': 576, 'center_order': 54, 'counter': 31, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '1152.157852', 'image_order': 1152, 'indicator': 1, 'kernel': '1152.a1', 'kernel_order': 27, 'label': '31104.fx.6e', 'nt': [12, 195], 'q_character': None, 'values': [[[6, 0]], [[2, 0]], [[-2, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-3, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]]]}
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id: 35404164
{'center': '576.a1', 'center_index': 576, 'center_order': 54, 'counter': 32, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '1152.157852', 'image_order': 1152, 'indicator': 1, 'kernel': '1152.a1', 'kernel_order': 27, 'label': '31104.fx.6f', 'nt': [12, 195], 'q_character': None, 'values': [[[6, 0]], [[2, 0]], [[-2, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-3, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]]]}
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id: 35404165
{'center': '108.a1', 'center_index': 108, 'center_order': 288, 'counter': 33, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '108.17', 'image_order': 108, 'indicator': 1, 'kernel': '108.a1', 'kernel_order': 288, 'label': '31104.fx.6g', 'nt': [18, 51], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[6, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]]]}
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id: 35404166
{'center': '108.a1', 'center_index': 108, 'center_order': 288, 'counter': 34, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '108.17', 'image_order': 108, 'indicator': 1, 'kernel': '108.a1', 'kernel_order': 288, 'label': '31104.fx.6h', 'nt': [18, 51], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-3, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35404167
{'center': '108.a1', 'center_index': 108, 'center_order': 288, 'counter': 35, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '216.102', 'image_order': 216, 'indicator': 1, 'kernel': '216.a1', 'kernel_order': 144, 'label': '31104.fx.6i', 'nt': [18, 94], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-6, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35404168
{'center': '108.a1', 'center_index': 108, 'center_order': 288, 'counter': 36, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '216.102', 'image_order': 216, 'indicator': 1, 'kernel': '216.a1', 'kernel_order': 144, 'label': '31104.fx.6j', 'nt': [18, 94], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-6, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[3, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35404169
{'center': '108.a1', 'center_index': 108, 'center_order': 288, 'counter': 37, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '216.102', 'image_order': 216, 'indicator': 1, 'kernel': '216.a1', 'kernel_order': 144, 'label': '31104.fx.6k', 'nt': [18, 94], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-6, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]]]}
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id: 35404170
{'center': '108.a1', 'center_index': 108, 'center_order': 288, 'counter': 38, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '216.102', 'image_order': 216, 'indicator': 1, 'kernel': '216.a1', 'kernel_order': 144, 'label': '31104.fx.6l', 'nt': [18, 94], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-6, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]]]}
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id: 35404171
{'center': '216.b1', 'center_index': 216, 'center_order': 144, 'counter': 39, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '216.162', 'image_order': 216, 'indicator': 1, 'kernel': '216.b1', 'kernel_order': 144, 'label': '31104.fx.8a', 'nt': [12, 117], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35404173
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id: 35404174
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id: 35404175
{'center': '576.a1', 'center_index': 576, 'center_order': 54, 'counter': 42, 'cyclotomic_n': 1, 'dim': 9, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '576.8654', 'image_order': 576, 'indicator': 1, 'kernel': '576.a1', 'kernel_order': 54, 'label': '31104.fx.9c', 'nt': [18, 185], 'q_character': None, 'values': [[[9, 0]], [[-3, 0]], [[1, 0]], [[9, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[9, 0]], [[9, 0]], [[9, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
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id: 35404176
{'center': '576.a1', 'center_index': 576, 'center_order': 54, 'counter': 43, 'cyclotomic_n': 1, 'dim': 9, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '576.8654', 'image_order': 576, 'indicator': 1, 'kernel': '576.a1', 'kernel_order': 54, 'label': '31104.fx.9d', 'nt': [18, 185], 'q_character': None, 'values': [[[9, 0]], [[-3, 0]], [[1, 0]], [[9, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[9, 0]], [[9, 0]], [[9, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[-3, 0]], [[-1, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
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id: 35404177
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id: 35404178
{'center': '576.a1', 'center_index': 576, 'center_order': 54, 'counter': 45, 'cyclotomic_n': 1, 'dim': 9, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '1152.157852', 'image_order': 1152, 'indicator': 1, 'kernel': '1152.a1', 'kernel_order': 27, 'label': '31104.fx.9f', 'nt': [18, 267], 'q_character': None, 'values': [[[9, 0]], [[-3, 0]], [[1, 0]], [[-9, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[9, 0]], [[9, 0]], [[9, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
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id: 35404179
{'center': '576.a1', 'center_index': 576, 'center_order': 54, 'counter': 46, 'cyclotomic_n': 1, 'dim': 9, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '1152.157852', 'image_order': 1152, 'indicator': 1, 'kernel': '1152.a1', 'kernel_order': 27, 'label': '31104.fx.9g', 'nt': [18, 267], 'q_character': None, 'values': [[[9, 0]], [[-3, 0]], [[1, 0]], [[-9, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[9, 0]], [[9, 0]], [[9, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[1, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
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id: 35404180
{'center': '576.a1', 'center_index': 576, 'center_order': 54, 'counter': 47, 'cyclotomic_n': 1, 'dim': 9, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '1152.157852', 'image_order': 1152, 'indicator': 1, 'kernel': '1152.a1', 'kernel_order': 27, 'label': '31104.fx.9h', 'nt': [18, 267], 'q_character': None, 'values': [[[9, 0]], [[-3, 0]], [[1, 0]], [[-9, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[9, 0]], [[9, 0]], [[9, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[-3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
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id: 35404181
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id: 35404182
{'center': '648.a1', 'center_index': 648, 'center_order': 48, 'counter': 49, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '648.555', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1', 'kernel_order': 48, 'label': '31104.fx.12b', 'nt': [18, 191], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[12, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[12, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]]]}
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id: 35404184
{'center': '1944.a1', 'center_index': 1944, 'center_order': 16, 'counter': 50, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '1944.2342', 'image_order': 1944, 'indicator': 1, 'kernel': '1944.a1', 'kernel_order': 16, 'label': '31104.fx.12c', 'nt': [18, 342], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35404185
{'center': '576.a1', 'center_index': 576, 'center_order': 54, 'counter': 51, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '576.8654', 'image_order': 576, 'indicator': 1, 'kernel': '576.a1', 'kernel_order': 54, 'label': '31104.fx.12d', 'nt': [24, 1503], 'q_character': None, 'values': [[[12, 0]], [[4, 0]], [[-4, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35404186
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id: 35404187
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id: 35404188
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id: 35404189
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id: 35404190
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id: 35404191
{'center': '3456.a1', 'center_index': 3456, 'center_order': 9, 'counter': 57, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '3456.di', 'image_order': 3456, 'indicator': 1, 'kernel': '3456.a1', 'kernel_order': 9, 'label': '31104.fx.12j', 'nt': [36, 4392], 'q_character': None, 'values': [[[12, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[-6, 0]], [[6, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]]]}
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id: 35404192
{'center': '31104.a1', 'center_index': 31104, 'center_order': 1, 'counter': 58, 'cyclotomic_n': 1, 'dim': 12, 'faithful': True, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '31104.fx', 'image_order': 31104, 'indicator': 1, 'kernel': '31104.a1', 'kernel_order': 1, 'label': '31104.fx.12k', 'nt': [36, 13453], 'q_character': None, 'values': [[[12, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-5, 0]], [[7, 0]], [[-2, 0]], [[2, 0]], [[8, 0]], [[2, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35404193
{'center': '31104.a1', 'center_index': 31104, 'center_order': 1, 'counter': 59, 'cyclotomic_n': 1, 'dim': 12, 'faithful': True, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '31104.fx', 'image_order': 31104, 'indicator': 1, 'kernel': '31104.a1', 'kernel_order': 1, 'label': '31104.fx.12l', 'nt': [36, 13455], 'q_character': None, 'values': [[[12, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-5, 0]], [[7, 0]], [[-2, 0]], [[2, 0]], [[8, 0]], [[2, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35404195
{'center': '3456.a1', 'center_index': 3456, 'center_order': 9, 'counter': 60, 'cyclotomic_n': 1, 'dim': 18, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '3456.di', 'image_order': 3456, 'indicator': 1, 'kernel': '3456.a1', 'kernel_order': 9, 'label': '31104.fx.18a', 'nt': [36, 4545], 'q_character': None, 'values': [[[18, 0]], [[-6, 0]], [[2, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[18, 0]], [[18, 0]], [[18, 0]], [[-9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[3, 0]], [[-1, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]]]}
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id: 35404196
{'center': '10368.a1', 'center_index': 10368, 'center_order': 3, 'counter': 61, 'cyclotomic_n': 1, 'dim': 18, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '10368.pi', 'image_order': 10368, 'indicator': 1, 'kernel': '10368.a1', 'kernel_order': 3, 'label': '31104.fx.18b', 'nt': [36, 9018], 'q_character': None, 'values': [[[18, 0]], [[-6, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[18, 0]], [[-9, 0]], [[-9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[2, 0]], [[8, 0]], [[-1, 0]], [[0, 0]], [[-4, 0]], [[8, 0]], [[-1, 0]], [[0, 0]], [[-4, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]]]}
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id: 35404197
{'center': '10368.a1', 'center_index': 10368, 'center_order': 3, 'counter': 62, 'cyclotomic_n': 1, 'dim': 18, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '10368.pi', 'image_order': 10368, 'indicator': 1, 'kernel': '10368.a1', 'kernel_order': 3, 'label': '31104.fx.18c', 'nt': [36, 9018], 'q_character': None, 'values': [[[18, 0]], [[-6, 0]], [[2, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-9, 0]], [[18, 0]], [[-9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-6, 0]], [[-1, 0]], [[8, 0]], [[2, 0]], [[0, 0]], [[8, 0]], [[-4, 0]], [[-1, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35404198
{'center': '3456.a1', 'center_index': 3456, 'center_order': 9, 'counter': 63, 'cyclotomic_n': 1, 'dim': 18, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '3456.di', 'image_order': 3456, 'indicator': 1, 'kernel': '3456.a1', 'kernel_order': 9, 'label': '31104.fx.18d', 'nt': [54, 0], 'q_character': None, 'values': [[[18, 0]], [[-6, 0]], [[2, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[18, 0]], [[18, 0]], [[18, 0]], [[-9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[3, 0]], [[-1, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]]]}
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id: 35404199
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id: 35404200
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id: 35404201
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id: 35404202
{'center': '10368.a1', 'center_index': 10368, 'center_order': 3, 'counter': 67, 'cyclotomic_n': 1, 'dim': 18, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '10368.pi', 'image_order': 10368, 'indicator': 1, 'kernel': '10368.a1', 'kernel_order': 3, 'label': '31104.fx.18h', 'nt': [54, 0], 'q_character': None, 'values': [[[18, 0]], [[-6, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[18, 0]], [[-9, 0]], [[-9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[2, 0]], [[8, 0]], [[-1, 0]], [[0, 0]], [[-4, 0]], [[8, 0]], [[-1, 0]], [[0, 0]], [[-4, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-4, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]]]}
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id: 35404203
{'center': '10368.a1', 'center_index': 10368, 'center_order': 3, 'counter': 68, 'cyclotomic_n': 1, 'dim': 18, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '10368.pi', 'image_order': 10368, 'indicator': 1, 'kernel': '10368.a1', 'kernel_order': 3, 'label': '31104.fx.18i', 'nt': [54, 0], 'q_character': None, 'values': [[[18, 0]], [[-6, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[6, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[18, 0]], [[-9, 0]], [[-9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[2, 0]], [[8, 0]], [[-1, 0]], [[0, 0]], [[-4, 0]], [[8, 0]], [[-1, 0]], [[0, 0]], [[-4, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]]]}
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id: 35404204
{'center': '10368.a1', 'center_index': 10368, 'center_order': 3, 'counter': 69, 'cyclotomic_n': 1, 'dim': 18, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '10368.pi', 'image_order': 10368, 'indicator': 1, 'kernel': '10368.a1', 'kernel_order': 3, 'label': '31104.fx.18j', 'nt': [54, 0], 'q_character': None, 'values': [[[18, 0]], [[-6, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[18, 0]], [[-9, 0]], [[-9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[2, 0]], [[8, 0]], [[-1, 0]], [[0, 0]], [[-4, 0]], [[8, 0]], [[-1, 0]], [[0, 0]], [[-4, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]]]}
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id: 35404206
{'center': '3456.a1', 'center_index': 3456, 'center_order': 9, 'counter': 70, 'cyclotomic_n': 1, 'dim': 18, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '3456.di', 'image_order': 3456, 'indicator': 1, 'kernel': '3456.a1', 'kernel_order': 9, 'label': '31104.fx.18k', 'nt': [54, 0], 'q_character': None, 'values': [[[18, 0]], [[-6, 0]], [[2, 0]], [[0, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[18, 0]], [[18, 0]], [[18, 0]], [[-9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[3, 0]], [[-1, 0]], [[-6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]]]}
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id: 35404207
{'center': '10368.a1', 'center_index': 10368, 'center_order': 3, 'counter': 71, 'cyclotomic_n': 1, 'dim': 18, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '10368.pi', 'image_order': 10368, 'indicator': 1, 'kernel': '10368.a1', 'kernel_order': 3, 'label': '31104.fx.18l', 'nt': [54, 0], 'q_character': None, 'values': [[[18, 0]], [[-6, 0]], [[2, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-9, 0]], [[18, 0]], [[-9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-6, 0]], [[-1, 0]], [[8, 0]], [[2, 0]], [[0, 0]], [[8, 0]], [[-4, 0]], [[-1, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35404208
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id: 35404209
{'center': '3456.a1', 'center_index': 3456, 'center_order': 9, 'counter': 73, 'cyclotomic_n': 1, 'dim': 24, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '3456.di', 'image_order': 3456, 'indicator': 1, 'kernel': '3456.a1', 'kernel_order': 9, 'label': '31104.fx.24b', 'nt': [48, 0], 'q_character': None, 'values': [[[24, 0]], [[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[24, 0]], [[24, 0]], [[24, 0]], [[-12, 0]], [[-6, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[-8, 0]], [[4, 0]], [[-8, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-8, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35404210
{'center': '31104.a1', 'center_index': 31104, 'center_order': 1, 'counter': 74, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '31104.fx', 'image_order': 31104, 'indicator': 1, 'kernel': '31104.a1', 'kernel_order': 1, 'label': '31104.fx.24c', 'nt': [72, 0], 'q_character': None, 'values': [[[24, 0]], [[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[-12, 0]], [[6, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-10, 0]], [[14, 0]], [[-4, 0]], [[4, 0]], [[16, 0]], [[4, 0]], [[8, 0]], [[-8, 0]], [[-8, 0]], [[-2, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35404211
{'center': '31104.a1', 'center_index': 31104, 'center_order': 1, 'counter': 75, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '31104.fx', 'image_order': 31104, 'indicator': 1, 'kernel': '31104.a1', 'kernel_order': 1, 'label': '31104.fx.24d', 'nt': [72, 0], 'q_character': None, 'values': [[[24, 0]], [[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[-12, 0]], [[6, 0]], [[0, 0]], [[12, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-10, 0]], [[14, 0]], [[-4, 0]], [[4, 0]], [[-8, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35404212
{'center': '31104.a1', 'center_index': 31104, 'center_order': 1, 'counter': 76, 'cyclotomic_n': 3, 'dim': 24, 'faithful': True, 'field': [1, -1, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '31104.fx', 'image_order': 31104, 'indicator': 0, 'kernel': '31104.a1', 'kernel_order': 1, 'label': '31104.fx.24e1', 'nt': [144, 0], 'q_character': None, 'values': [[[24, 0]], [[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[-12, 0]], [[6, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-10, 0]], [[14, 0]], [[-4, 0]], [[4, 0]], [[-8, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-4, 0], [-6, 1]], [[-1, 0]], [[2, 0], [6, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35404213
{'center': '31104.a1', 'center_index': 31104, 'center_order': 1, 'counter': 77, 'cyclotomic_n': 3, 'dim': 24, 'faithful': True, 'field': [1, -1, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '31104.fx', 'image_order': 31104, 'indicator': 0, 'kernel': '31104.a1', 'kernel_order': 1, 'label': '31104.fx.24e2', 'nt': [144, 2], 'q_character': None, 'values': [[[24, 0]], [[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[-12, 0]], [[6, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-10, 0]], [[14, 0]], [[-4, 0]], [[4, 0]], [[-8, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0], [6, 1]], [[-1, 0]], [[-4, 0], [-6, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35404214
{'center': '10368.a1', 'center_index': 10368, 'center_order': 3, 'counter': 78, 'cyclotomic_n': 1, 'dim': 36, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '10368.pi', 'image_order': 10368, 'indicator': 1, 'kernel': '10368.a1', 'kernel_order': 3, 'label': '31104.fx.36a', 'nt': [72, 0], 'q_character': None, 'values': [[[36, 0]], [[-12, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[36, 0]], [[-18, 0]], [[-18, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[4, 0]], [[-8, 0]], [[-2, 0]], [[0, 0]], [[4, 0]], [[-8, 0]], [[-2, 0]], [[0, 0]], [[4, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35404215
{'center': '10368.a1', 'center_index': 10368, 'center_order': 3, 'counter': 79, 'cyclotomic_n': 1, 'dim': 36, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '10368.pi', 'image_order': 10368, 'indicator': 1, 'kernel': '10368.a1', 'kernel_order': 3, 'label': '31104.fx.36b', 'nt': [72, 0], 'q_character': None, 'values': [[[36, 0]], [[-12, 0]], [[4, 0]], [[0, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-18, 0]], [[36, 0]], [[-18, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-12, 0]], [[-2, 0]], [[-8, 0]], [[4, 0]], [[0, 0]], [[-8, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35404217
{'center': '31104.a1', 'center_index': 31104, 'center_order': 1, 'counter': 80, 'cyclotomic_n': 1, 'dim': 36, 'faithful': True, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '31104.fx', 'image_order': 31104, 'indicator': 1, 'kernel': '31104.a1', 'kernel_order': 1, 'label': '31104.fx.36c', 'nt': [72, 0], 'q_character': None, 'values': [[[36, 0]], [[12, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-18, 0]], [[-18, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[21, 0]], [[-15, 0]], [[-6, 0]], [[6, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35404218
{'center': '10368.a1', 'center_index': 10368, 'center_order': 3, 'counter': 81, 'cyclotomic_n': 1, 'dim': 36, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '10368.pi', 'image_order': 10368, 'indicator': 1, 'kernel': '10368.a1', 'kernel_order': 3, 'label': '31104.fx.36d', 'nt': [72, 0], 'q_character': None, 'values': [[[36, 0]], [[12, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-18, 0]], [[36, 0]], [[-18, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[12, 0]], [[6, 0]], [[0, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35404219
{'center': '10368.a1', 'center_index': 10368, 'center_order': 3, 'counter': 82, 'cyclotomic_n': 1, 'dim': 36, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '10368.pi', 'image_order': 10368, 'indicator': 1, 'kernel': '10368.a1', 'kernel_order': 3, 'label': '31104.fx.36e', 'nt': [72, 0], 'q_character': None, 'values': [[[36, 0]], [[12, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[36, 0]], [[-18, 0]], [[-18, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-12, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35404220
{'center': '10368.a1', 'center_index': 10368, 'center_order': 3, 'counter': 83, 'cyclotomic_n': 1, 'dim': 36, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '10368.pi', 'image_order': 10368, 'indicator': 1, 'kernel': '10368.a1', 'kernel_order': 3, 'label': '31104.fx.36f', 'nt': [108, 0], 'q_character': None, 'values': [[[36, 0]], [[-12, 0]], [[4, 0]], [[0, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-18, 0]], [[36, 0]], [[-18, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-12, 0]], [[-2, 0]], [[-8, 0]], [[4, 0]], [[0, 0]], [[-8, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35404221
{'center': '10368.a1', 'center_index': 10368, 'center_order': 3, 'counter': 84, 'cyclotomic_n': 1, 'dim': 36, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '10368.pi', 'image_order': 10368, 'indicator': 1, 'kernel': '10368.a1', 'kernel_order': 3, 'label': '31104.fx.36g', 'nt': [108, 0], 'q_character': None, 'values': [[[36, 0]], [[-12, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[36, 0]], [[-18, 0]], [[-18, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[4, 0]], [[-8, 0]], [[-2, 0]], [[0, 0]], [[4, 0]], [[-8, 0]], [[-2, 0]], [[0, 0]], [[4, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35404222
{'center': '31104.a1', 'center_index': 31104, 'center_order': 1, 'counter': 85, 'cyclotomic_n': 1, 'dim': 36, 'faithful': True, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '31104.fx', 'image_order': 31104, 'indicator': 1, 'kernel': '31104.a1', 'kernel_order': 1, 'label': '31104.fx.36h', 'nt': [108, 0], 'q_character': None, 'values': [[[36, 0]], [[-12, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-18, 0]], [[-18, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-2, 0]], [[-8, 0]], [[-2, 0]], [[12, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[-6, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35404223
{'center': '31104.a1', 'center_index': 31104, 'center_order': 1, 'counter': 86, 'cyclotomic_n': 1, 'dim': 36, 'faithful': True, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '31104.fx', 'image_order': 31104, 'indicator': 1, 'kernel': '31104.a1', 'kernel_order': 1, 'label': '31104.fx.36i', 'nt': [108, 0], 'q_character': None, 'values': [[[36, 0]], [[-12, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-18, 0]], [[-18, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-2, 0]], [[-8, 0]], [[-2, 0]], [[12, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[-6, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35404224
{'center': '31104.a1', 'center_index': 31104, 'center_order': 1, 'counter': 87, 'cyclotomic_n': 1, 'dim': 36, 'faithful': True, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '31104.fx', 'image_order': 31104, 'indicator': 1, 'kernel': '31104.a1', 'kernel_order': 1, 'label': '31104.fx.36j', 'nt': [108, 0], 'q_character': None, 'values': [[[36, 0]], [[12, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-18, 0]], [[-18, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[21, 0]], [[-15, 0]], [[-6, 0]], [[6, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35404225
{'center': '10368.a1', 'center_index': 10368, 'center_order': 3, 'counter': 88, 'cyclotomic_n': 1, 'dim': 36, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '10368.pi', 'image_order': 10368, 'indicator': 1, 'kernel': '10368.a1', 'kernel_order': 3, 'label': '31104.fx.36k', 'nt': [108, 0], 'q_character': None, 'values': [[[36, 0]], [[12, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-18, 0]], [[36, 0]], [[-18, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[12, 0]], [[6, 0]], [[0, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35404226
{'center': '10368.a1', 'center_index': 10368, 'center_order': 3, 'counter': 89, 'cyclotomic_n': 1, 'dim': 36, 'faithful': False, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '10368.pi', 'image_order': 10368, 'indicator': 1, 'kernel': '10368.a1', 'kernel_order': 3, 'label': '31104.fx.36l', 'nt': [108, 0], 'q_character': None, 'values': [[[36, 0]], [[12, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[36, 0]], [[-18, 0]], [[-18, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-12, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35404228
{'center': '31104.a1', 'center_index': 31104, 'center_order': 1, 'counter': 90, 'cyclotomic_n': 1, 'dim': 72, 'faithful': True, 'field': [0, 1], 'group': '31104.fx', 'group_counter': 154, 'group_order': 31104, 'image': None, 'image_isoclass': '31104.fx', 'image_order': 31104, 'indicator': 1, 'kernel': '31104.a1', 'kernel_order': 1, 'label': '31104.fx.72a', 'nt': [216, 0], 'q_character': None, 'values': [[[72, 0]], [[-24, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-36, 0]], [[-36, 0]], [[18, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[-6, 0]], [[-6, 0]], [[12, 0]], [[-4, 0]], [[8, 0]], [[-4, 0]], [[-12, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[6, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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gps_subgroup_search • Show schema
Hide schema
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id: 186245335
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 31104, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '31104.fx.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1', 'outer_equivalence': True, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0', 'R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '31104.fx', 'subgroup_hash': 4394578261467941646, 'subgroup_order': 31104, 'subgroup_tex': '(C_2^2\\times C_6^2).S_3^3', 'supersolvable': False, 'sylow': 0}
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id: 186246446
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 15552, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '31104.fx.2.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '15552.ea', 'subgroup_hash': 7658633754316149407, 'subgroup_order': 15552, 'subgroup_tex': '(C_3^2\\times A_4^2):D_6', 'supersolvable': False, 'sylow': 0}
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id: 186247557
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 15552, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '31104.fx.2.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 3173828342764885090, 'subgroup_order': 15552, 'subgroup_tex': 'C_2^4.C_3^4.D_6', 'supersolvable': False, 'sylow': 0}
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id: 186248057
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 15552, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '31104.fx.2.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '15552.el', 'subgroup_hash': 1079981536618394854, 'subgroup_order': 15552, 'subgroup_tex': '(C_2\\times C_6^3):S_3^2', 'supersolvable': False, 'sylow': 0}
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id: 186248168
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 15552, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '31104.fx.2.d1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '15552.dm', 'subgroup_hash': 950499389268693354, 'subgroup_order': 15552, 'subgroup_tex': '(C_2\\times C_6^3):S_3^2', 'supersolvable': False, 'sylow': 0}
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id: 186248279
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 15552, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '31104.fx.2.e1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1', 'C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '15552.ep', 'subgroup_hash': 3255377266310984154, 'subgroup_order': 15552, 'subgroup_tex': '(C_2\\times C_6^3):S_3^2', 'supersolvable': False, 'sylow': 0}
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id: 186248390
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 5184, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10368.fj', 'subgroup_hash': 5002487537532140962, 'subgroup_order': 10368, 'subgroup_tex': 'A_4^2:(S_3\\times D_6)', 'supersolvable': False, 'sylow': 0}
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id: 186248501
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 5184, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3.b1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10368.je', 'subgroup_hash': 6228584704245755470, 'subgroup_order': 10368, 'subgroup_tex': 'C_6^2.(D_6\\times S_4)', 'supersolvable': False, 'sylow': 0}
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id: 186248612
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 7776, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '31104.fx.4.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 178039435414573188, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^3.A_4^2.C_2', 'supersolvable': False, 'sylow': 0}
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id: 186245336
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 7776, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '31104.fx.4.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '7776.dc', 'subgroup_hash': 7794371425270113477, 'subgroup_order': 7776, 'subgroup_tex': '(C_3^2\\times A_4^2):C_6', 'supersolvable': False, 'sylow': 0}
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id: 186245447
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 7776, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '31104.fx.4.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '7776.do', 'subgroup_hash': 30649388718912511, 'subgroup_order': 7776, 'subgroup_tex': '(C_3^2\\times A_4^2):S_3', 'supersolvable': False, 'sylow': 0}
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id: 186245558
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 7776, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '31104.fx.4.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 8355023171303878239, 'subgroup_order': 7776, 'subgroup_tex': 'C_2^4.C_3^4.S_3', 'supersolvable': False, 'sylow': 0}
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id: 186245669
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 7776, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '31104.fx.4.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2', 'C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 2097944158335202142, 'subgroup_order': 7776, 'subgroup_tex': 'C_2^4.C_3^4.C_6', 'supersolvable': False, 'sylow': 0}
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id: 186245780
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 5184, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '31104.fx.6.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '5184.iq', 'subgroup_hash': 7327890083507694818, 'subgroup_order': 5184, 'subgroup_tex': 'C_6^2:(S_3\\times S_4)', 'supersolvable': False, 'sylow': 0}
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id: 186245891
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 5184, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '31104.fx.6.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '5184.gh', 'subgroup_hash': 4546247329692833486, 'subgroup_order': 5184, 'subgroup_tex': 'A_4^2:S_3^2', 'supersolvable': False, 'sylow': 0}
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id: 186246002
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 2592, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.6.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5184.gn', 'subgroup_hash': 2051125435053010653, 'subgroup_order': 5184, 'subgroup_tex': 'A_4^2:S_3^2', 'supersolvable': False, 'sylow': 0}
-
id: 186246113
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 2592, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.6.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5184.rt', 'subgroup_hash': 3651664466133988184, 'subgroup_order': 5184, 'subgroup_tex': '(A_4\\times C_6^2):D_6', 'supersolvable': False, 'sylow': 0}
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id: 186246224
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 2592, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.6.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5184.ib', 'subgroup_hash': 4339839685880800741, 'subgroup_order': 5184, 'subgroup_tex': 'C_6^2.(A_4\\times D_6)', 'supersolvable': False, 'sylow': 0}
-
id: 186246335
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 864, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.6.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6536312426235821005, 'subgroup_order': 5184, 'subgroup_tex': 'C_6^2.(S_3\\times C_3:D_4)', 'supersolvable': False, 'sylow': 0}
-
id: 186246447
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 2592, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.6.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 703403591151733561, 'subgroup_order': 5184, 'subgroup_tex': 'C_2^4.C_3^3:S_3.C_2', 'supersolvable': False, 'sylow': 0}
-
id: 186246558
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 2592, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.6.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5184.it', 'subgroup_hash': 8211553804654759977, 'subgroup_order': 5184, 'subgroup_tex': '(S_3\\times C_6^2):S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186246669
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 2592, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.6.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5184.if', 'subgroup_hash': 104564251599197432, 'subgroup_order': 5184, 'subgroup_tex': '(C_2\\times C_6^3):D_6', 'supersolvable': False, 'sylow': 0}
-
id: 186246780
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 2592, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.6.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5184.gg', 'subgroup_hash': 6460910484686728448, 'subgroup_order': 5184, 'subgroup_tex': 'C_3\\times A_4^2:D_6', 'supersolvable': False, 'sylow': 0}
-
id: 186246891
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 864, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.6.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5184.hu', 'subgroup_hash': 2385449411715820399, 'subgroup_order': 5184, 'subgroup_tex': 'C_3^2.\\POPlus(4,3)', 'supersolvable': False, 'sylow': 0}
-
id: 186247002
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 2592, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.6.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5184.hx', 'subgroup_hash': 4408017417877629614, 'subgroup_order': 5184, 'subgroup_tex': '(S_3\\times C_6^2):S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186247113
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 2592, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.6.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5184.gh', 'subgroup_hash': 4546247329692833486, 'subgroup_order': 5184, 'subgroup_tex': 'A_4^2:S_3^2', 'supersolvable': False, 'sylow': 0}
-
id: 186247224
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 2592, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.6.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5184.iz', 'subgroup_hash': 7319934086923406458, 'subgroup_order': 5184, 'subgroup_tex': '(C_2\\times C_6^3):D_6', 'supersolvable': False, 'sylow': 0}
-
id: 186247335
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 3888, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '31104.fx.8.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C3', 'D', 'L1', 'D1', 'C3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 2770698895795212788, 'subgroup_order': 3888, 'subgroup_tex': 'C_2^4.C_3^4.C_3', 'supersolvable': False, 'sylow': 0}
-
id: 186247446
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.8.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1656309622519700539, 'subgroup_order': 3888, 'subgroup_tex': 'C_6^2.C_3^3.C_2^2', 'supersolvable': False, 'sylow': 0}
-
id: 186247558
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 288, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.9.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3456.di', 'subgroup_hash': 9016919946097627263, 'subgroup_order': 3456, 'subgroup_tex': 'C_2^4:S_3^3', 'supersolvable': False, 'sylow': 0}
-
id: 186247669
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 288, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.9.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3456.gu', 'subgroup_hash': 3056348276295266572, 'subgroup_order': 3456, 'subgroup_tex': 'C_6^2.(C_2^2\\times S_4)', 'supersolvable': False, 'sylow': 0}
-
id: 186247780
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 864, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.9.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3456.de', 'subgroup_hash': 5423518584134085580, 'subgroup_order': 3456, 'subgroup_tex': 'D_6^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186247891
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 864, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.9.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3456.cj', 'subgroup_hash': 821882546282671655, 'subgroup_order': 3456, 'subgroup_tex': 'C_2^4:S_3^3', 'supersolvable': True, 'sylow': 0}
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id: 186247991
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 2592, 'counter': 34, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '31104.fx.12.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1550641336008583382, 'subgroup_order': 2592, 'subgroup_tex': '(C_2\\times C_6^3).C_6', 'supersolvable': False, 'sylow': 0}
-
id: 186248002
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 2592, 'counter': 35, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '31104.fx.12.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2592.ge', 'subgroup_hash': 782330867239566636, 'subgroup_order': 2592, 'subgroup_tex': 'C_3\\times C_6^2:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186248013
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 2592, 'counter': 36, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '31104.fx.12.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2592.fk', 'subgroup_hash': 8682297689292649312, 'subgroup_order': 2592, 'subgroup_tex': '(C_3\\times A_4)\\wr C_2', 'supersolvable': False, 'sylow': 0}
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id: 186248024
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 2592, 'counter': 37, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '31104.fx.12.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2592.gv', 'subgroup_hash': 1245281944090543677, 'subgroup_order': 2592, 'subgroup_tex': '(C_3\\times C_6^2):S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248035
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 2592, 'counter': 38, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '31104.fx.12.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2592.pd', 'subgroup_hash': 1003551817112337500, 'subgroup_order': 2592, 'subgroup_tex': '(A_4\\times C_6^2):S_3', 'supersolvable': False, 'sylow': 0}
-
id: 186248046
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.12.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 8540676996724437484, 'subgroup_order': 2592, 'subgroup_tex': 'C_2\\times C_6^2.S_3^2', 'supersolvable': False, 'sylow': 0}
-
id: 186248058
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.12.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6357518762973070256, 'subgroup_order': 2592, 'subgroup_tex': 'C_6^2.C_3^2:C_4.C_2', 'supersolvable': False, 'sylow': 0}
-
id: 186248069
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.12.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 8245374156140175690, 'subgroup_order': 2592, 'subgroup_tex': 'C_6^2:C_3.C_3:D_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248080
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.12.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6637875517798423096, 'subgroup_order': 2592, 'subgroup_tex': 'C_6^2.D_6:S_3', 'supersolvable': False, 'sylow': 0}
-
id: 186248091
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1296, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.12.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2592.oh', 'subgroup_hash': 5477753825663678181, 'subgroup_order': 2592, 'subgroup_tex': 'C_3:S_3\\times A_4^2', 'supersolvable': False, 'sylow': 0}
-
id: 186248102
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 864, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.12.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5572245030814639737, 'subgroup_order': 2592, 'subgroup_tex': 'C_2\\times C_3.C_6^2:C_6.C_2', 'supersolvable': False, 'sylow': 0}
-
id: 186248113
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1296, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.12.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2592.gc', 'subgroup_hash': 1504250334108372163, 'subgroup_order': 2592, 'subgroup_tex': '(C_2\\times C_6^3):C_6', 'supersolvable': False, 'sylow': 0}
-
id: 186248124
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 864, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.12.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2592.gg', 'subgroup_hash': 278589153638914516, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^2.A_4\\wr C_2', 'supersolvable': False, 'sylow': 0}
-
id: 186248135
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1296, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.12.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2592.ga', 'subgroup_hash': 2596389148190241817, 'subgroup_order': 2592, 'subgroup_tex': '(C_2\\times C_6^3):C_6', 'supersolvable': False, 'sylow': 0}
-
id: 186248146
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1296, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.12.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2592.fk', 'subgroup_hash': 8682297689292649312, 'subgroup_order': 2592, 'subgroup_tex': '(C_3\\times A_4)\\wr C_2', 'supersolvable': False, 'sylow': 0}
-
id: 186248157
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 432, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.12.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2592.gg', 'subgroup_hash': 278589153638914516, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^2.A_4\\wr C_2', 'supersolvable': False, 'sylow': 0}
-
id: 186248169
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 432, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.12.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 8650833876124980607, 'subgroup_order': 2592, 'subgroup_tex': 'C_3\\times C_6^2:C_3.D_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248180
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1296, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.12.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 4768831874684242305, 'subgroup_order': 2592, 'subgroup_tex': 'C_3\\times C_2^4:\\He_3.C_2', 'supersolvable': False, 'sylow': 0}
-
id: 186248191
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 144, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.12.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1378586081979088867, 'subgroup_order': 2592, 'subgroup_tex': 'C_3\\times C_2^4.C_3^2:S_3', 'supersolvable': False, 'sylow': 0}
-
id: 186248202
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1296, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.12.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2592.og', 'subgroup_hash': 1414665040929205306, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^2\\times \\PSOPlus(4,3)', 'supersolvable': False, 'sylow': 0}
-
id: 186248213
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 432, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.12.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1378586081979088867, 'subgroup_order': 2592, 'subgroup_tex': 'C_3\\times C_2^4.C_3^2:S_3', 'supersolvable': False, 'sylow': 0}
-
id: 186248224
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 432, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.12.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 4579918442815492123, 'subgroup_order': 2592, 'subgroup_tex': '(C_3\\times C_6\\times A_4).C_6.C_2', 'supersolvable': False, 'sylow': 0}
-
id: 186248235
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1296, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.12.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 2961804796783368495, 'subgroup_order': 2592, 'subgroup_tex': 'C_2^4.C_3^3:S_3', 'supersolvable': False, 'sylow': 0}
-
id: 186248246
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.12.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2592.jb', 'subgroup_hash': 6898096242996517164, 'subgroup_order': 2592, 'subgroup_tex': 'S_3\\times C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
-
id: 186248257
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.16.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.2592', 'subgroup_hash': 2592, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^3:(C_6\\times A_4)', 'supersolvable': False, 'sylow': 0}
-
id: 186248268
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.16.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.2512', 'subgroup_hash': 2512, 'subgroup_order': 1944, 'subgroup_tex': '(A_4\\times C_3^3):S_3', 'supersolvable': False, 'sylow': 0}
-
id: 186248280
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.16.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.2463', 'subgroup_hash': 2463, 'subgroup_order': 1944, 'subgroup_tex': '(A_4\\times C_3^3):C_6', 'supersolvable': False, 'sylow': 0}
-
id: 186248291
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.16.d1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.2342', 'subgroup_hash': 2342, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^2.S_3^3', 'supersolvable': True, 'sylow': 0}
-
id: 186248302
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.18.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.23041', 'subgroup_hash': 23041, 'subgroup_order': 1728, 'subgroup_tex': 'C_2^3.S_3^3', 'supersolvable': True, 'sylow': 0}
-
id: 186248313
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.18.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.47413', 'subgroup_hash': 47413, 'subgroup_order': 1728, 'subgroup_tex': 'C_2^3:S_3^3', 'supersolvable': True, 'sylow': 0}
-
id: 186248324
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.18.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.23041', 'subgroup_hash': 23041, 'subgroup_order': 1728, 'subgroup_tex': 'C_2^3.S_3^3', 'supersolvable': True, 'sylow': 0}
-
id: 186248335
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.18.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.23050', 'subgroup_hash': 23050, 'subgroup_order': 1728, 'subgroup_tex': 'C_2^3.S_3^3', 'supersolvable': True, 'sylow': 0}
-
id: 186248346
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.18.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.23050', 'subgroup_hash': 23050, 'subgroup_order': 1728, 'subgroup_tex': 'C_2^3.S_3^3', 'supersolvable': True, 'sylow': 0}
-
id: 186248357
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.18.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.23054', 'subgroup_hash': 23054, 'subgroup_order': 1728, 'subgroup_tex': 'C_2^3.S_3^3', 'supersolvable': True, 'sylow': 0}
-
id: 186248368
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 144, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.18.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.47858', 'subgroup_hash': 47858, 'subgroup_order': 1728, 'subgroup_tex': 'A_4^2:D_6', 'supersolvable': False, 'sylow': 0}
-
id: 186248379
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 288, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.18.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.47858', 'subgroup_hash': 47858, 'subgroup_order': 1728, 'subgroup_tex': 'A_4^2:D_6', 'supersolvable': False, 'sylow': 0}
-
id: 186248391
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 144, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.18.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.47859', 'subgroup_hash': 47859, 'subgroup_order': 1728, 'subgroup_tex': 'A_4^2:D_6', 'supersolvable': False, 'sylow': 0}
-
id: 186248402
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.18.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.47859', 'subgroup_hash': 47859, 'subgroup_order': 1728, 'subgroup_tex': 'A_4^2:D_6', 'supersolvable': False, 'sylow': 0}
-
id: 186248413
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 144, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.18.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.13285', 'subgroup_hash': 13285, 'subgroup_order': 1728, 'subgroup_tex': 'C_6^2.(C_2^2\\times A_4)', 'supersolvable': False, 'sylow': 0}
-
id: 186248424
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 432, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.18.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.32233', 'subgroup_hash': 32233, 'subgroup_order': 1728, 'subgroup_tex': 'D_6^2:A_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248435
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 288, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.18.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.46119', 'subgroup_hash': 46119, 'subgroup_order': 1728, 'subgroup_tex': 'C_6^2:(C_2\\times S_4)', 'supersolvable': False, 'sylow': 0}
-
id: 186248446
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 864, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.18.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.47900', 'subgroup_hash': 47900, 'subgroup_order': 1728, 'subgroup_tex': 'C_6^2:(C_2\\times S_4)', 'supersolvable': False, 'sylow': 0}
-
id: 186248457
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.18.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.46848', 'subgroup_hash': 46848, 'subgroup_order': 1728, 'subgroup_tex': 'C_3:S_3\\times \\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
-
id: 186248468
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 432, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.18.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.47898', 'subgroup_hash': 47898, 'subgroup_order': 1728, 'subgroup_tex': 'C_6^2:(C_2\\times S_4)', 'supersolvable': False, 'sylow': 0}
-
id: 186248479
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 144, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.18.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.46119', 'subgroup_hash': 46119, 'subgroup_order': 1728, 'subgroup_tex': 'C_6^2:(C_2\\times S_4)', 'supersolvable': False, 'sylow': 0}
-
id: 186248490
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.18.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.30324', 'subgroup_hash': 30324, 'subgroup_order': 1728, 'subgroup_tex': 'C_6^2:(C_2\\times S_4)', 'supersolvable': False, 'sylow': 0}
-
id: 186248502
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 864, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.18.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.44171', 'subgroup_hash': 44171, 'subgroup_order': 1728, 'subgroup_tex': 'C_6^3.C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 186248513
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 864, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.18.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.44171', 'subgroup_hash': 44171, 'subgroup_order': 1728, 'subgroup_tex': 'C_6^3.C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 186248524
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 144, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.18.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.13074', 'subgroup_hash': 13074, 'subgroup_order': 1728, 'subgroup_tex': '(C_2\\times C_6^2):S_4', 'supersolvable': False, 'sylow': 0}
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id: 186248535
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 144, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.18.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.47854', 'subgroup_hash': 47854, 'subgroup_order': 1728, 'subgroup_tex': 'C_3\\times \\POPlus(4,3)', 'supersolvable': False, 'sylow': 0}
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id: 186248546
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 432, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.18.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.24805', 'subgroup_hash': 24805, 'subgroup_order': 1728, 'subgroup_tex': 'C_6^3.C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 186248557
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 432, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.18.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.31983', 'subgroup_hash': 31983, 'subgroup_order': 1728, 'subgroup_tex': 'C_3\\times C_2^4:S_3^2', 'supersolvable': False, 'sylow': 0}
-
id: 186248568
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 144, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.18.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.31983', 'subgroup_hash': 31983, 'subgroup_order': 1728, 'subgroup_tex': 'C_3\\times C_2^4:S_3^2', 'supersolvable': False, 'sylow': 0}
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id: 186248579
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 432, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.18.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.24805', 'subgroup_hash': 24805, 'subgroup_order': 1728, 'subgroup_tex': 'C_6^3.C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 186248590
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 864, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.18.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.31983', 'subgroup_hash': 31983, 'subgroup_order': 1728, 'subgroup_tex': 'C_3\\times C_2^4:S_3^2', 'supersolvable': False, 'sylow': 0}
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id: 186248601
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 288, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.18.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.12469', 'subgroup_hash': 12469, 'subgroup_order': 1728, 'subgroup_tex': '(C_2^2\\times C_6^2):D_6', 'supersolvable': False, 'sylow': 0}
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id: 186248613
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 288, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.18.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.47855', 'subgroup_hash': 47855, 'subgroup_order': 1728, 'subgroup_tex': 'A_4^2:D_6', 'supersolvable': False, 'sylow': 0}
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id: 186248624
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 288, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.18.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.46101', 'subgroup_hash': 46101, 'subgroup_order': 1728, 'subgroup_tex': 'C_3.\\POPlus(4,3)', 'supersolvable': False, 'sylow': 0}
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id: 186248635
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 288, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.18.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.12894', 'subgroup_hash': 12894, 'subgroup_order': 1728, 'subgroup_tex': '(C_2\\times C_6^2):S_4', 'supersolvable': False, 'sylow': 0}
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id: 186248646
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 288, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.18.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.47856', 'subgroup_hash': 47856, 'subgroup_order': 1728, 'subgroup_tex': 'A_4^2:D_6', 'supersolvable': False, 'sylow': 0}
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id: 186248657
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 864, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.18.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.32131', 'subgroup_hash': 32131, 'subgroup_order': 1728, 'subgroup_tex': '(C_6\\times D_6):S_4', 'supersolvable': False, 'sylow': 0}
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id: 186248668
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 48, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.18.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.47856', 'subgroup_hash': 47856, 'subgroup_order': 1728, 'subgroup_tex': 'A_4^2:D_6', 'supersolvable': False, 'sylow': 0}
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id: 186248679
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 144, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.18.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.47856', 'subgroup_hash': 47856, 'subgroup_order': 1728, 'subgroup_tex': 'A_4^2:D_6', 'supersolvable': False, 'sylow': 0}
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id: 186248690
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 432, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.18.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.32131', 'subgroup_hash': 32131, 'subgroup_order': 1728, 'subgroup_tex': '(C_6\\times D_6):S_4', 'supersolvable': False, 'sylow': 0}
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id: 186248701
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 144, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.18.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.12469', 'subgroup_hash': 12469, 'subgroup_order': 1728, 'subgroup_tex': '(C_2^2\\times C_6^2):D_6', 'supersolvable': False, 'sylow': 0}
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id: 186248712
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 48, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.18.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.12469', 'subgroup_hash': 12469, 'subgroup_order': 1728, 'subgroup_tex': '(C_2^2\\times C_6^2):D_6', 'supersolvable': False, 'sylow': 0}
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id: 186245337
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 432, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.18.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.28127', 'subgroup_hash': 28127, 'subgroup_order': 1728, 'subgroup_tex': 'C_6^3.C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 186245348
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1296, 'counter': 101, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '31104.fx.24.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': ['C4'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3061', 'subgroup_hash': 3061, 'subgroup_order': 1296, 'subgroup_tex': 'C_3\\times C_6^2:A_4', 'supersolvable': False, 'sylow': 0}
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id: 186245359
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 1296, 'counter': 102, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '31104.fx.24.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': ['C4', 'C4'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3557', 'subgroup_hash': 3557, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^2\\times A_4^2', 'supersolvable': False, 'sylow': 0}
-
id: 186245370
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.24.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3551', 'subgroup_hash': 3551, 'subgroup_order': 1296, 'subgroup_tex': 'C_6^2:S_3^2', 'supersolvable': False, 'sylow': 0}
-
id: 186245381
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.24.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.2498', 'subgroup_hash': 2498, 'subgroup_order': 1296, 'subgroup_tex': 'C_6^2:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245392
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.24.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.2940', 'subgroup_hash': 2940, 'subgroup_order': 1296, 'subgroup_tex': 'C_6^2:S_3^2', 'supersolvable': False, 'sylow': 0}
-
id: 186245403
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.24.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.2940', 'subgroup_hash': 2940, 'subgroup_order': 1296, 'subgroup_tex': 'C_6^2:S_3^2', 'supersolvable': False, 'sylow': 0}
-
id: 186245414
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.24.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.2940', 'subgroup_hash': 2940, 'subgroup_order': 1296, 'subgroup_tex': 'C_6^2:S_3^2', 'supersolvable': False, 'sylow': 0}
-
id: 186245425
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.24.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3024', 'subgroup_hash': 3024, 'subgroup_order': 1296, 'subgroup_tex': 'C_6^3:C_6', 'supersolvable': False, 'sylow': 0}
-
id: 186245436
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 27, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.24.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3002', 'subgroup_hash': 3002, 'subgroup_order': 1296, 'subgroup_tex': 'C_6^3:S_3', 'supersolvable': False, 'sylow': 0}
-
id: 186245448
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.24.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3024', 'subgroup_hash': 3024, 'subgroup_order': 1296, 'subgroup_tex': 'C_6^3:C_6', 'supersolvable': False, 'sylow': 0}
-
id: 186245459
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.24.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3003', 'subgroup_hash': 3003, 'subgroup_order': 1296, 'subgroup_tex': 'C_6^3:S_3', 'supersolvable': False, 'sylow': 0}
-
id: 186245470
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 27, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.24.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.2130', 'subgroup_hash': 2130, 'subgroup_order': 1296, 'subgroup_tex': 'C_6^3.S_3', 'supersolvable': False, 'sylow': 0}
-
id: 186245481
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.24.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.2131', 'subgroup_hash': 2131, 'subgroup_order': 1296, 'subgroup_tex': 'C_6^3.S_3', 'supersolvable': False, 'sylow': 0}
-
id: 186245492
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 432, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.24.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3051', 'subgroup_hash': 3051, 'subgroup_order': 1296, 'subgroup_tex': 'C_6^3:C_6', 'supersolvable': False, 'sylow': 0}
-
id: 186245503
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 144, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.24.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.2960', 'subgroup_hash': 2960, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^2.A_4^2', 'supersolvable': False, 'sylow': 0}
-
id: 186245514
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 432, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.24.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.2960', 'subgroup_hash': 2960, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^2.A_4^2', 'supersolvable': False, 'sylow': 0}
-
id: 186245525
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.24.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.2945', 'subgroup_hash': 2945, 'subgroup_order': 1296, 'subgroup_tex': 'C_6^2:C_6\\times S_3', 'supersolvable': False, 'sylow': 0}
-
id: 186245536
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.24.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.2928', 'subgroup_hash': 2928, 'subgroup_order': 1296, 'subgroup_tex': 'C_6^2:S_3^2', 'supersolvable': False, 'sylow': 0}
-
id: 186245547
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.24.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.2940', 'subgroup_hash': 2940, 'subgroup_order': 1296, 'subgroup_tex': 'C_6^2:S_3^2', 'supersolvable': False, 'sylow': 0}
-
id: 186245559
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.24.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.2934', 'subgroup_hash': 2934, 'subgroup_order': 1296, 'subgroup_tex': 'C_6^2:S_3^2', 'supersolvable': False, 'sylow': 0}
-
id: 186245570
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.24.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.2923', 'subgroup_hash': 2923, 'subgroup_order': 1296, 'subgroup_tex': 'C_6^2.S_3^2', 'supersolvable': False, 'sylow': 0}
-
id: 186245581
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.24.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.2924', 'subgroup_hash': 2924, 'subgroup_order': 1296, 'subgroup_tex': 'C_6^2:S_3^2', 'supersolvable': False, 'sylow': 0}
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id: 186245592
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.24.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.2933', 'subgroup_hash': 2933, 'subgroup_order': 1296, 'subgroup_tex': 'C_6^2.S_3^2', 'supersolvable': False, 'sylow': 0}
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id: 186245603
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.27.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1152.157852', 'subgroup_hash': 4208954026111918128, 'subgroup_order': 1152, 'subgroup_tex': 'A_4^2:C_2^3', 'supersolvable': False, 'sylow': 0}
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id: 186245614
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 48, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.27.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1152.155790', 'subgroup_hash': 6460622858988636210, 'subgroup_order': 1152, 'subgroup_tex': 'S_3\\times C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186245625
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 288, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.27.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1152.155790', 'subgroup_hash': 6460622858988636210, 'subgroup_order': 1152, 'subgroup_tex': 'S_3\\times C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186245636
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.27.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1152.99265', 'subgroup_hash': 4963667966820280558, 'subgroup_order': 1152, 'subgroup_tex': 'D_6^2:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186245647
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.27.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1152.99265', 'subgroup_hash': 4963667966820280558, 'subgroup_order': 1152, 'subgroup_tex': 'D_6^2:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186245658
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.32.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.564', 'subgroup_hash': 564, 'subgroup_order': 972, 'subgroup_tex': 'C_6^2:\\He_3', 'supersolvable': False, 'sylow': 0}
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id: 186245670
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.32.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.428', 'subgroup_hash': 428, 'subgroup_order': 972, 'subgroup_tex': 'C_3^4:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245681
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.32.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.456', 'subgroup_hash': 456, 'subgroup_order': 972, 'subgroup_tex': 'C_3^4:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245692
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.32.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.455', 'subgroup_hash': 455, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245703
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.32.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.427', 'subgroup_hash': 427, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186245714
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.32.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.474', 'subgroup_hash': 474, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186245725
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 864, 'counter': 135, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '31104.fx.36.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '36.10', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '864.4724', 'subgroup_hash': 4724, 'subgroup_order': 864, 'subgroup_tex': 'C_6^3:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245736
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 864, 'counter': 136, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '31104.fx.36.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '36.10', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '864.4709', 'subgroup_hash': 4709, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186245747
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4406', 'subgroup_hash': 4406, 'subgroup_order': 864, 'subgroup_tex': 'C_2^2:S_3^3', 'supersolvable': True, 'sylow': 0}
-
id: 186245758
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4378', 'subgroup_hash': 4378, 'subgroup_order': 864, 'subgroup_tex': 'C_6.D_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245769
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4386', 'subgroup_hash': 4386, 'subgroup_order': 864, 'subgroup_tex': 'C_6.D_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245781
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4387', 'subgroup_hash': 4387, 'subgroup_order': 864, 'subgroup_tex': 'C_6.D_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245792
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4577', 'subgroup_hash': 4577, 'subgroup_order': 864, 'subgroup_tex': 'C_6^3:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245803
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4577', 'subgroup_hash': 4577, 'subgroup_order': 864, 'subgroup_tex': 'C_6^3:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245814
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.3594', 'subgroup_hash': 3594, 'subgroup_order': 864, 'subgroup_tex': 'C_6^3.C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245825
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.3594', 'subgroup_hash': 3594, 'subgroup_order': 864, 'subgroup_tex': 'C_6^3.C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245836
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4525', 'subgroup_hash': 4525, 'subgroup_order': 864, 'subgroup_tex': 'C_6^3:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245847
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.3605', 'subgroup_hash': 3605, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186245858
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.1963', 'subgroup_hash': 1963, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2.D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186245869
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.1963', 'subgroup_hash': 1963, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2.D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186245880
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4525', 'subgroup_hash': 4525, 'subgroup_order': 864, 'subgroup_tex': 'C_6^3:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245892
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.3606', 'subgroup_hash': 3606, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186245903
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.1964', 'subgroup_hash': 1964, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2.D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186245914
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.2050', 'subgroup_hash': 2050, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2.D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186245925
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4600', 'subgroup_hash': 4600, 'subgroup_order': 864, 'subgroup_tex': 'C_6^3:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245936
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.3605', 'subgroup_hash': 3605, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186245947
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.1963', 'subgroup_hash': 1963, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2.D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186245958
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.3606', 'subgroup_hash': 3606, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186245969
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.1964', 'subgroup_hash': 1964, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2.D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186245980
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.2050', 'subgroup_hash': 2050, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2.D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186245991
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4691', 'subgroup_hash': 4691, 'subgroup_order': 864, 'subgroup_tex': 'C_6:S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246003
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4000', 'subgroup_hash': 4000, 'subgroup_order': 864, 'subgroup_tex': 'C_2\\times C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
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id: 186246014
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4155', 'subgroup_hash': 4155, 'subgroup_order': 864, 'subgroup_tex': 'C_6.(S_3\\times S_4)', 'supersolvable': False, 'sylow': 0}
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id: 186246025
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.2235', 'subgroup_hash': 2235, 'subgroup_order': 864, 'subgroup_tex': 'C_6.(S_3\\times S_4)', 'supersolvable': False, 'sylow': 0}
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id: 186246036
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4577', 'subgroup_hash': 4577, 'subgroup_order': 864, 'subgroup_tex': 'C_6^3:C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 186246047
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.3594', 'subgroup_hash': 3594, 'subgroup_order': 864, 'subgroup_tex': 'C_6^3.C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 186246058
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4156', 'subgroup_hash': 4156, 'subgroup_order': 864, 'subgroup_tex': 'C_3^2:\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
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id: 186246069
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.3605', 'subgroup_hash': 3605, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246080
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.2238', 'subgroup_hash': 2238, 'subgroup_order': 864, 'subgroup_tex': 'C_3^2:\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
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id: 186246091
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.2239', 'subgroup_hash': 2239, 'subgroup_order': 864, 'subgroup_tex': 'C_3^2:\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
-
id: 186246102
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4157', 'subgroup_hash': 4157, 'subgroup_order': 864, 'subgroup_tex': 'C_3^2:\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
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id: 186246114
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.3606', 'subgroup_hash': 3606, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246125
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 144, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4680', 'subgroup_hash': 4680, 'subgroup_order': 864, 'subgroup_tex': 'S_3\\times A_4^2', 'supersolvable': False, 'sylow': 0}
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id: 186246136
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4680', 'subgroup_hash': 4680, 'subgroup_order': 864, 'subgroup_tex': 'S_3\\times A_4^2', 'supersolvable': False, 'sylow': 0}
-
id: 186246147
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 144, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4030', 'subgroup_hash': 4030, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:(C_2\\times A_4)', 'supersolvable': False, 'sylow': 0}
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id: 186246158
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4712', 'subgroup_hash': 4712, 'subgroup_order': 864, 'subgroup_tex': 'C_6:D_6\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 186246169
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 432, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4714', 'subgroup_hash': 4714, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:(C_2\\times A_4)', 'supersolvable': False, 'sylow': 0}
-
id: 186246180
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4026', 'subgroup_hash': 4026, 'subgroup_order': 864, 'subgroup_tex': 'C_2^2\\times C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
-
id: 186246191
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 144, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.1315', 'subgroup_hash': 1315, 'subgroup_order': 864, 'subgroup_tex': '(C_2\\times C_6^2):A_4', 'supersolvable': False, 'sylow': 0}
-
id: 186246202
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 144, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4676', 'subgroup_hash': 4676, 'subgroup_order': 864, 'subgroup_tex': 'A_4^2:C_6', 'supersolvable': False, 'sylow': 0}
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id: 186246213
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 432, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.3789', 'subgroup_hash': 3789, 'subgroup_order': 864, 'subgroup_tex': 'C_6^3.C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 186246225
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 432, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.3023', 'subgroup_hash': 3023, 'subgroup_order': 864, 'subgroup_tex': '(C_6\\times D_6):A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246236
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 144, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.3023', 'subgroup_hash': 3023, 'subgroup_order': 864, 'subgroup_tex': '(C_6\\times D_6):A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246247
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 288, 'counter': 182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4019', 'subgroup_hash': 4019, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186246258
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 288, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4677', 'subgroup_hash': 4677, 'subgroup_order': 864, 'subgroup_tex': 'A_4^2:S_3', 'supersolvable': False, 'sylow': 0}
-
id: 186246269
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 288, 'counter': 184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.3992', 'subgroup_hash': 3992, 'subgroup_order': 864, 'subgroup_tex': 'C_3.A_4\\wr C_2', 'supersolvable': False, 'sylow': 0}
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id: 186246280
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 48, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4676', 'subgroup_hash': 4676, 'subgroup_order': 864, 'subgroup_tex': 'A_4^2:C_6', 'supersolvable': False, 'sylow': 0}
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id: 186246291
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 144, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4676', 'subgroup_hash': 4676, 'subgroup_order': 864, 'subgroup_tex': 'A_4^2:C_6', 'supersolvable': False, 'sylow': 0}
-
id: 186246302
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 432, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.3023', 'subgroup_hash': 3023, 'subgroup_order': 864, 'subgroup_tex': '(C_6\\times D_6):A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246313
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 144, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4022', 'subgroup_hash': 4022, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186246324
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 144, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.736', 'subgroup_hash': 736, 'subgroup_order': 864, 'subgroup_tex': '(C_2^2\\times C_6^2):C_6', 'supersolvable': False, 'sylow': 0}
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id: 186246336
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 48, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4022', 'subgroup_hash': 4022, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186246347
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 48, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.736', 'subgroup_hash': 736, 'subgroup_order': 864, 'subgroup_tex': '(C_2^2\\times C_6^2):C_6', 'supersolvable': False, 'sylow': 0}
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id: 186246358
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 48, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4677', 'subgroup_hash': 4677, 'subgroup_order': 864, 'subgroup_tex': 'A_4^2:S_3', 'supersolvable': False, 'sylow': 0}
-
id: 186246369
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 144, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4677', 'subgroup_hash': 4677, 'subgroup_order': 864, 'subgroup_tex': 'A_4^2:S_3', 'supersolvable': False, 'sylow': 0}
-
id: 186246380
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 144, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.3992', 'subgroup_hash': 3992, 'subgroup_order': 864, 'subgroup_tex': 'C_3.A_4\\wr C_2', 'supersolvable': False, 'sylow': 0}
-
id: 186246391
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 48, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.3992', 'subgroup_hash': 3992, 'subgroup_order': 864, 'subgroup_tex': 'C_3.A_4\\wr C_2', 'supersolvable': False, 'sylow': 0}
-
id: 186246402
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 432, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.3875', 'subgroup_hash': 3875, 'subgroup_order': 864, 'subgroup_tex': 'C_6^3.C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186246413
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 432, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4709', 'subgroup_hash': 4709, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186246424
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 144, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4709', 'subgroup_hash': 4709, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186246435
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 432, 'counter': 199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.3789', 'subgroup_hash': 3789, 'subgroup_order': 864, 'subgroup_tex': 'C_6^3.C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186246448
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 144, 'counter': 200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4418', 'subgroup_hash': 4418, 'subgroup_order': 864, 'subgroup_tex': 'C_3^2\\times \\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
-
id: 186246459
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 432, 'counter': 201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4708', 'subgroup_hash': 4708, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186246470
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 144, 'counter': 202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4418', 'subgroup_hash': 4418, 'subgroup_order': 864, 'subgroup_tex': 'C_3^2\\times \\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
-
id: 186246481
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 144, 'counter': 203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4708', 'subgroup_hash': 4708, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186246492
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 144, 'counter': 204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4022', 'subgroup_hash': 4022, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186246503
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 144, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4678', 'subgroup_hash': 4678, 'subgroup_order': 864, 'subgroup_tex': 'A_4^2:C_6', 'supersolvable': False, 'sylow': 0}
-
id: 186246514
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 144, 'counter': 206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.3996', 'subgroup_hash': 3996, 'subgroup_order': 864, 'subgroup_tex': '(C_3\\times A_4):S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186246525
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 16, 'counter': 207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.2365', 'subgroup_hash': 2365, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186246536
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 16, 'counter': 208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.3996', 'subgroup_hash': 3996, 'subgroup_order': 864, 'subgroup_tex': '(C_3\\times A_4):S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186246547
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 16, 'counter': 209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4678', 'subgroup_hash': 4678, 'subgroup_order': 864, 'subgroup_tex': 'A_4^2:C_6', 'supersolvable': False, 'sylow': 0}
-
id: 186246559
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 144, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4019', 'subgroup_hash': 4019, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186246570
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 48, 'counter': 211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4019', 'subgroup_hash': 4019, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186246581
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 432, 'counter': 212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.3875', 'subgroup_hash': 3875, 'subgroup_order': 864, 'subgroup_tex': 'C_6^3.C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186246592
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.2332', 'subgroup_hash': 2332, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186246603
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.2332', 'subgroup_hash': 2332, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186246614
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 48, 'counter': 215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4679', 'subgroup_hash': 4679, 'subgroup_order': 864, 'subgroup_tex': 'A_4^2:S_3', 'supersolvable': False, 'sylow': 0}
-
id: 186246625
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 144, 'counter': 216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4679', 'subgroup_hash': 4679, 'subgroup_order': 864, 'subgroup_tex': 'A_4^2:S_3', 'supersolvable': False, 'sylow': 0}
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id: 186246636
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4440', 'subgroup_hash': 4440, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186246647
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 432, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4710', 'subgroup_hash': 4710, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186246658
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4679', 'subgroup_hash': 4679, 'subgroup_order': 864, 'subgroup_tex': 'A_4^2:S_3', 'supersolvable': False, 'sylow': 0}
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id: 186246670
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4679', 'subgroup_hash': 4679, 'subgroup_order': 864, 'subgroup_tex': 'A_4^2:S_3', 'supersolvable': False, 'sylow': 0}
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id: 186246681
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4000', 'subgroup_hash': 4000, 'subgroup_order': 864, 'subgroup_tex': 'C_2\\times C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
-
id: 186246692
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4673', 'subgroup_hash': 4673, 'subgroup_order': 864, 'subgroup_tex': 'S_4\\times S_3^2', 'supersolvable': False, 'sylow': 0}
-
id: 186246703
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4378', 'subgroup_hash': 4378, 'subgroup_order': 864, 'subgroup_tex': 'C_6.D_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186246714
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4406', 'subgroup_hash': 4406, 'subgroup_order': 864, 'subgroup_tex': 'C_2^2:S_3^3', 'supersolvable': True, 'sylow': 0}
-
id: 186246725
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4387', 'subgroup_hash': 4387, 'subgroup_order': 864, 'subgroup_tex': 'C_6.D_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186246736
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.36.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4386', 'subgroup_hash': 4386, 'subgroup_order': 864, 'subgroup_tex': 'C_6.D_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186246747
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.48.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.610', 'subgroup_hash': 610, 'subgroup_order': 648, 'subgroup_tex': 'C_2\\times C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186246758
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.48.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.420', 'subgroup_hash': 420, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:(C_4\\times S_3)', 'supersolvable': True, 'sylow': 0}
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id: 186246769
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.48.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.423', 'subgroup_hash': 423, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246781
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.48.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.421', 'subgroup_hash': 421, 'subgroup_order': 648, 'subgroup_tex': '\\He_3:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246792
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.48.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.740', 'subgroup_hash': 740, 'subgroup_order': 648, 'subgroup_tex': 'C_3\\times C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
-
id: 186246803
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.48.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.630', 'subgroup_hash': 630, 'subgroup_order': 648, 'subgroup_tex': 'C_2\\times C_3^3:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186246814
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.48.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.594', 'subgroup_hash': 594, 'subgroup_order': 648, 'subgroup_tex': '(C_3\\times C_6^2):C_6', 'supersolvable': False, 'sylow': 0}
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id: 186246825
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.48.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.594', 'subgroup_hash': 594, 'subgroup_order': 648, 'subgroup_tex': '(C_3\\times C_6^2):C_6', 'supersolvable': False, 'sylow': 0}
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id: 186246836
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 27, 'counter': 235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.48.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.497', 'subgroup_hash': 497, 'subgroup_order': 648, 'subgroup_tex': 'C_3\\times C_6^2:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246847
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 27, 'counter': 236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.48.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.572', 'subgroup_hash': 572, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246858
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.48.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.572', 'subgroup_hash': 572, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246869
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.48.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.572', 'subgroup_hash': 572, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246880
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.48.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.572', 'subgroup_hash': 572, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246892
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.48.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.736', 'subgroup_hash': 736, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246903
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.48.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.572', 'subgroup_hash': 572, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246914
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.48.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.594', 'subgroup_hash': 594, 'subgroup_order': 648, 'subgroup_tex': '(C_3\\times C_6^2):C_6', 'supersolvable': False, 'sylow': 0}
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id: 186246925
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.48.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.496', 'subgroup_hash': 496, 'subgroup_order': 648, 'subgroup_tex': '(C_3\\times C_6^2):C_6', 'supersolvable': True, 'sylow': 0}
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id: 186246936
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.48.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.573', 'subgroup_hash': 573, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246947
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.48.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.573', 'subgroup_hash': 573, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246958
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.48.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.738', 'subgroup_hash': 738, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246969
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.48.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.621', 'subgroup_hash': 621, 'subgroup_order': 648, 'subgroup_tex': 'C_6^3:C_3', 'supersolvable': False, 'sylow': 0}
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id: 186246980
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.48.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.594', 'subgroup_hash': 594, 'subgroup_order': 648, 'subgroup_tex': '(C_3\\times C_6^2):C_6', 'supersolvable': False, 'sylow': 0}
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id: 186246991
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.48.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.587', 'subgroup_hash': 587, 'subgroup_order': 648, 'subgroup_tex': 'S_3\\times C_3^2:A_4', 'supersolvable': False, 'sylow': 0}
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id: 186247003
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.48.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.561', 'subgroup_hash': 561, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186247014
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.48.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.586', 'subgroup_hash': 586, 'subgroup_order': 648, 'subgroup_tex': 'C_3\\times C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
-
id: 186247025
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.48.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.577', 'subgroup_hash': 577, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186247036
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.48.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.572', 'subgroup_hash': 572, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186247047
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.48.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.573', 'subgroup_hash': 573, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186247058
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.48.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.734', 'subgroup_hash': 734, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
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id: 186247069
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.48.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.555', 'subgroup_hash': 555, 'subgroup_order': 648, 'subgroup_tex': 'C_3.S_3^3', 'supersolvable': True, 'sylow': 0}
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id: 186247080
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.3409', 'subgroup_hash': 3409, 'subgroup_order': 576, 'subgroup_tex': '(C_6\\times D_4).D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247091
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.2286', 'subgroup_hash': 2286, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247102
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.2286', 'subgroup_hash': 2286, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247114
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8557', 'subgroup_hash': 8557, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 186247125
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8557', 'subgroup_hash': 8557, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186247136
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.3409', 'subgroup_hash': 3409, 'subgroup_order': 576, 'subgroup_tex': '(C_6\\times D_4).D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247147
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.2286', 'subgroup_hash': 2286, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247158
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.3413', 'subgroup_hash': 3413, 'subgroup_order': 576, 'subgroup_tex': '(C_2\\times C_{12}):D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186247169
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.3413', 'subgroup_hash': 3413, 'subgroup_order': 576, 'subgroup_tex': '(C_2\\times C_{12}):D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186247180
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.2292', 'subgroup_hash': 2292, 'subgroup_order': 576, 'subgroup_tex': '(C_2\\times D_6):D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186247191
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 267, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.3413', 'subgroup_hash': 3413, 'subgroup_order': 576, 'subgroup_tex': '(C_2\\times C_{12}):D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186247202
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.2292', 'subgroup_hash': 2292, 'subgroup_order': 576, 'subgroup_tex': '(C_2\\times D_6):D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186247213
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.2292', 'subgroup_hash': 2292, 'subgroup_order': 576, 'subgroup_tex': '(C_2\\times D_6):D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186247225
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.2292', 'subgroup_hash': 2292, 'subgroup_order': 576, 'subgroup_tex': '(C_2\\times D_6):D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186247236
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 271, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8656', 'subgroup_hash': 8656, 'subgroup_order': 576, 'subgroup_tex': 'A_4^2:C_2^2', 'supersolvable': False, 'sylow': 0}
-
id: 186247247
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 272, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8657', 'subgroup_hash': 8657, 'subgroup_order': 576, 'subgroup_tex': 'A_4^2:C_2^2', 'supersolvable': False, 'sylow': 0}
-
id: 186247258
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 144, 'counter': 273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5562', 'subgroup_hash': 5562, 'subgroup_order': 576, 'subgroup_tex': 'S_3\\times C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
-
id: 186247269
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 48, 'counter': 274, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5562', 'subgroup_hash': 5562, 'subgroup_order': 576, 'subgroup_tex': 'S_3\\times C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
-
id: 186247280
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 48, 'counter': 275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8660', 'subgroup_hash': 8660, 'subgroup_order': 576, 'subgroup_tex': 'C_2^4:S_3^2', 'supersolvable': False, 'sylow': 0}
-
id: 186247291
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 288, 'counter': 276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8660', 'subgroup_hash': 8660, 'subgroup_order': 576, 'subgroup_tex': 'C_2^4:S_3^2', 'supersolvable': False, 'sylow': 0}
-
id: 186247302
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8353', 'subgroup_hash': 8353, 'subgroup_order': 576, 'subgroup_tex': 'S_3\\times \\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
-
id: 186247313
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 48, 'counter': 278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8660', 'subgroup_hash': 8660, 'subgroup_order': 576, 'subgroup_tex': 'C_2^4:S_3^2', 'supersolvable': False, 'sylow': 0}
-
id: 186247324
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 144, 'counter': 279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8660', 'subgroup_hash': 8660, 'subgroup_order': 576, 'subgroup_tex': 'C_2^4:S_3^2', 'supersolvable': False, 'sylow': 0}
-
id: 186247336
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 280, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8353', 'subgroup_hash': 8353, 'subgroup_order': 576, 'subgroup_tex': 'S_3\\times \\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
-
id: 186247347
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8353', 'subgroup_hash': 8353, 'subgroup_order': 576, 'subgroup_tex': 'S_3\\times \\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
-
id: 186247358
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8660', 'subgroup_hash': 8660, 'subgroup_order': 576, 'subgroup_tex': 'C_2^4:S_3^2', 'supersolvable': False, 'sylow': 0}
-
id: 186247369
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.7941', 'subgroup_hash': 7941, 'subgroup_order': 576, 'subgroup_tex': 'C_6^2.C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 186247380
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.7409', 'subgroup_hash': 7409, 'subgroup_order': 576, 'subgroup_tex': 'C_2^4:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186247391
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 285, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.7409', 'subgroup_hash': 7409, 'subgroup_order': 576, 'subgroup_tex': 'C_2^4:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186247402
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 286, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.7941', 'subgroup_hash': 7941, 'subgroup_order': 576, 'subgroup_tex': 'C_6^2.C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 186247413
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.7409', 'subgroup_hash': 7409, 'subgroup_order': 576, 'subgroup_tex': 'C_2^4:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186247424
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 288, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.7409', 'subgroup_hash': 7409, 'subgroup_order': 576, 'subgroup_tex': 'C_2^4:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186247435
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 48, 'counter': 289, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.4011', 'subgroup_hash': 4011, 'subgroup_order': 576, 'subgroup_tex': 'C_3\\times C_2^4:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247447
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 144, 'counter': 290, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5464', 'subgroup_hash': 5464, 'subgroup_order': 576, 'subgroup_tex': 'C_3\\times C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186247458
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 48, 'counter': 291, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5464', 'subgroup_hash': 5464, 'subgroup_order': 576, 'subgroup_tex': 'C_3\\times C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186247469
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 48, 'counter': 292, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5464', 'subgroup_hash': 5464, 'subgroup_order': 576, 'subgroup_tex': 'C_3\\times C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186247480
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 144, 'counter': 293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.4011', 'subgroup_hash': 4011, 'subgroup_order': 576, 'subgroup_tex': 'C_3\\times C_2^4:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247491
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 16, 'counter': 294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8654', 'subgroup_hash': 8654, 'subgroup_order': 576, 'subgroup_tex': '\\POPlus(4,3)', 'supersolvable': False, 'sylow': 0}
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id: 186247502
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 48, 'counter': 295, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.3607', 'subgroup_hash': 3607, 'subgroup_order': 576, 'subgroup_tex': 'C_2^4:S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186247513
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 48, 'counter': 296, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5126', 'subgroup_hash': 5126, 'subgroup_order': 576, 'subgroup_tex': 'C_2^4:S_3^2', 'supersolvable': False, 'sylow': 0}
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id: 186247524
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 48, 'counter': 297, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5126', 'subgroup_hash': 5126, 'subgroup_order': 576, 'subgroup_tex': 'C_2^4:S_3^2', 'supersolvable': False, 'sylow': 0}
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id: 186247535
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 48, 'counter': 298, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.4011', 'subgroup_hash': 4011, 'subgroup_order': 576, 'subgroup_tex': 'C_3\\times C_2^4:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247546
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 48, 'counter': 299, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5126', 'subgroup_hash': 5126, 'subgroup_order': 576, 'subgroup_tex': 'C_2^4:S_3^2', 'supersolvable': False, 'sylow': 0}
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id: 186247559
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 144, 'counter': 300, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.3607', 'subgroup_hash': 3607, 'subgroup_order': 576, 'subgroup_tex': 'C_2^4:S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186247570
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 301, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8654', 'subgroup_hash': 8654, 'subgroup_order': 576, 'subgroup_tex': '\\POPlus(4,3)', 'supersolvable': False, 'sylow': 0}
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id: 186247581
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 302, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8654', 'subgroup_hash': 8654, 'subgroup_order': 576, 'subgroup_tex': '\\POPlus(4,3)', 'supersolvable': False, 'sylow': 0}
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id: 186247592
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 288, 'counter': 303, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5126', 'subgroup_hash': 5126, 'subgroup_order': 576, 'subgroup_tex': 'C_2^4:S_3^2', 'supersolvable': False, 'sylow': 0}
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id: 186247603
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 288, 'counter': 304, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5512', 'subgroup_hash': 5512, 'subgroup_order': 576, 'subgroup_tex': '(C_2^2\\times C_6):S_4', 'supersolvable': False, 'sylow': 0}
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id: 186247614
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 144, 'counter': 305, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5126', 'subgroup_hash': 5126, 'subgroup_order': 576, 'subgroup_tex': 'C_2^4:S_3^2', 'supersolvable': False, 'sylow': 0}
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id: 186247625
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 48, 'counter': 306, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5126', 'subgroup_hash': 5126, 'subgroup_order': 576, 'subgroup_tex': 'C_2^4:S_3^2', 'supersolvable': False, 'sylow': 0}
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id: 186247636
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 307, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.3607', 'subgroup_hash': 3607, 'subgroup_order': 576, 'subgroup_tex': 'C_2^4:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186247647
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 308, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8654', 'subgroup_hash': 8654, 'subgroup_order': 576, 'subgroup_tex': '\\POPlus(4,3)', 'supersolvable': False, 'sylow': 0}
-
id: 186247658
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 309, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8654', 'subgroup_hash': 8654, 'subgroup_order': 576, 'subgroup_tex': '\\POPlus(4,3)', 'supersolvable': False, 'sylow': 0}
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id: 186247670
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 310, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8654', 'subgroup_hash': 8654, 'subgroup_order': 576, 'subgroup_tex': '\\POPlus(4,3)', 'supersolvable': False, 'sylow': 0}
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id: 186247681
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 311, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8654', 'subgroup_hash': 8654, 'subgroup_order': 576, 'subgroup_tex': '\\POPlus(4,3)', 'supersolvable': False, 'sylow': 0}
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id: 186247692
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 48, 'counter': 312, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5512', 'subgroup_hash': 5512, 'subgroup_order': 576, 'subgroup_tex': '(C_2^2\\times C_6):S_4', 'supersolvable': False, 'sylow': 0}
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id: 186247703
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 313, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.54.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.3607', 'subgroup_hash': 3607, 'subgroup_order': 576, 'subgroup_tex': 'C_2^4:S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186247714
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 314, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.64.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.103', 'subgroup_hash': 103, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247725
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 315, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.64.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.102', 'subgroup_hash': 102, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247736
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 316, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.64.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.145', 'subgroup_hash': 145, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247747
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 317, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.64.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.183', 'subgroup_hash': 183, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247758
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 318, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.64.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.146', 'subgroup_hash': 146, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247769
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': True, 'core_order': 432, 'counter': 319, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '31104.fx.72.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '72.46', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_6', 'simple': False, 'solvable': True, 'special_labels': ['F', 'F'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '432.775', 'subgroup_hash': 775, 'subgroup_order': 432, 'subgroup_tex': 'C_2\\times C_6^3', 'supersolvable': True, 'sylow': 0}
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id: 186247781
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 432, 'counter': 320, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '31104.fx.72.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '72.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '72.46', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_6', 'simple': False, 'solvable': True, 'special_labels': ['C5', 'C5'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '432.771', 'subgroup_hash': 771, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:A_4', 'supersolvable': False, 'sylow': 0}
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id: 186247792
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 321, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.686', 'subgroup_hash': 686, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247803
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 322, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.686', 'subgroup_hash': 686, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247814
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 323, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.686', 'subgroup_hash': 686, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247825
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 324, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.768', 'subgroup_hash': 768, 'subgroup_order': 432, 'subgroup_tex': 'C_3:D_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186247836
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 325, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.679', 'subgroup_hash': 679, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247847
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 326, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.679', 'subgroup_hash': 679, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247858
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 327, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.658', 'subgroup_hash': 658, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247869
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 328, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.686', 'subgroup_hash': 686, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247880
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 329, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.652', 'subgroup_hash': 652, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247892
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 330, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.659', 'subgroup_hash': 659, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247903
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 331, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.653', 'subgroup_hash': 653, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247914
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 332, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.696', 'subgroup_hash': 696, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247925
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 333, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.693', 'subgroup_hash': 693, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247936
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 334, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.681', 'subgroup_hash': 681, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247947
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 335, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.681', 'subgroup_hash': 681, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247958
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 336, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.682', 'subgroup_hash': 682, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247969
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 337, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.451', 'subgroup_hash': 451, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247980
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 338, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.451', 'subgroup_hash': 451, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247990
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 339, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.682', 'subgroup_hash': 682, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247992
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 340, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.451', 'subgroup_hash': 451, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247993
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 54, 'counter': 341, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.774', 'subgroup_hash': 774, 'subgroup_order': 432, 'subgroup_tex': 'C_6^3:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 186247994
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 342, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.709', 'subgroup_hash': 709, 'subgroup_order': 432, 'subgroup_tex': 'D_6:C_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 186247995
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 343, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.719', 'subgroup_hash': 719, 'subgroup_order': 432, 'subgroup_tex': 'C_6^3:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 186247996
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 344, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.709', 'subgroup_hash': 709, 'subgroup_order': 432, 'subgroup_tex': 'D_6:C_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 186247997
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 345, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.774', 'subgroup_hash': 774, 'subgroup_order': 432, 'subgroup_tex': 'C_6^3:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 186247998
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 346, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.719', 'subgroup_hash': 719, 'subgroup_order': 432, 'subgroup_tex': 'C_6^3:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 186247999
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 347, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.479', 'subgroup_hash': 479, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186248000
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 348, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.479', 'subgroup_hash': 479, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186248001
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 349, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.495', 'subgroup_hash': 495, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186248003
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 350, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.495', 'subgroup_hash': 495, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186248004
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 351, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.747', 'subgroup_hash': 747, 'subgroup_order': 432, 'subgroup_tex': 'A_4:S_3^2', 'supersolvable': False, 'sylow': 0}
-
id: 186248005
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 352, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.747', 'subgroup_hash': 747, 'subgroup_order': 432, 'subgroup_tex': 'A_4:S_3^2', 'supersolvable': False, 'sylow': 0}
-
id: 186248006
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 353, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.747', 'subgroup_hash': 747, 'subgroup_order': 432, 'subgroup_tex': 'A_4:S_3^2', 'supersolvable': False, 'sylow': 0}
-
id: 186248007
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 354, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.685', 'subgroup_hash': 685, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186248008
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 355, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.746', 'subgroup_hash': 746, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
-
id: 186248009
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 356, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.746', 'subgroup_hash': 746, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
-
id: 186248010
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 357, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.523', 'subgroup_hash': 523, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
-
id: 186248011
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 358, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.323', 'subgroup_hash': 323, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186248012
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 359, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.523', 'subgroup_hash': 523, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
-
id: 186248014
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 360, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.686', 'subgroup_hash': 686, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186248015
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 361, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.746', 'subgroup_hash': 746, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
-
id: 186248016
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 362, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.686', 'subgroup_hash': 686, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186248017
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 363, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.523', 'subgroup_hash': 523, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
-
id: 186248018
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 364, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.764', 'subgroup_hash': 764, 'subgroup_order': 432, 'subgroup_tex': 'C_6:S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248019
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 365, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.542', 'subgroup_hash': 542, 'subgroup_order': 432, 'subgroup_tex': 'C_2\\times C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
-
id: 186248020
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 366, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.542', 'subgroup_hash': 542, 'subgroup_order': 432, 'subgroup_tex': 'C_2\\times C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
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id: 186248021
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 54, 'counter': 367, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.774', 'subgroup_hash': 774, 'subgroup_order': 432, 'subgroup_tex': 'C_6^3:C_2', 'supersolvable': True, 'sylow': 0}
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id: 186248022
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 368, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.709', 'subgroup_hash': 709, 'subgroup_order': 432, 'subgroup_tex': 'D_6:C_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186248023
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 369, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.760', 'subgroup_hash': 760, 'subgroup_order': 432, 'subgroup_tex': 'A_4:C_6^2', 'supersolvable': False, 'sylow': 0}
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id: 186248025
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 370, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.760', 'subgroup_hash': 760, 'subgroup_order': 432, 'subgroup_tex': 'A_4:C_6^2', 'supersolvable': False, 'sylow': 0}
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id: 186248026
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 371, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.538', 'subgroup_hash': 538, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
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id: 186248027
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 372, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.764', 'subgroup_hash': 764, 'subgroup_order': 432, 'subgroup_tex': 'C_6:S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186248028
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 373, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.542', 'subgroup_hash': 542, 'subgroup_order': 432, 'subgroup_tex': 'C_2\\times C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
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id: 186248029
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 374, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.542', 'subgroup_hash': 542, 'subgroup_order': 432, 'subgroup_tex': 'C_2\\times C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
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id: 186248030
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 375, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.774', 'subgroup_hash': 774, 'subgroup_order': 432, 'subgroup_tex': 'C_6^3:C_2', 'supersolvable': True, 'sylow': 0}
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id: 186248031
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 376, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.719', 'subgroup_hash': 719, 'subgroup_order': 432, 'subgroup_tex': 'C_6^3:C_2', 'supersolvable': True, 'sylow': 0}
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id: 186248032
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 377, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.535', 'subgroup_hash': 535, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
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id: 186248033
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 378, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.535', 'subgroup_hash': 535, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
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id: 186248034
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 379, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.762', 'subgroup_hash': 762, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
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id: 186248036
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 380, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.479', 'subgroup_hash': 479, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186248037
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 381, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.495', 'subgroup_hash': 495, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186248038
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 382, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.615', 'subgroup_hash': 615, 'subgroup_order': 432, 'subgroup_tex': 'C_3\\times A_4:C_{12}', 'supersolvable': False, 'sylow': 0}
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id: 186248039
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 383, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.621', 'subgroup_hash': 621, 'subgroup_order': 432, 'subgroup_tex': '(C_3^2\\times A_4):C_4', 'supersolvable': False, 'sylow': 0}
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id: 186248040
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 384, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.615', 'subgroup_hash': 615, 'subgroup_order': 432, 'subgroup_tex': 'C_3\\times A_4:C_{12}', 'supersolvable': False, 'sylow': 0}
-
id: 186248041
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 385, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.260', 'subgroup_hash': 260, 'subgroup_order': 432, 'subgroup_tex': '(C_3\\times C_6).S_4', 'supersolvable': False, 'sylow': 0}
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id: 186248042
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 386, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.251', 'subgroup_hash': 251, 'subgroup_order': 432, 'subgroup_tex': '(C_3\\times A_4):C_{12}', 'supersolvable': False, 'sylow': 0}
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id: 186248043
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 387, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.251', 'subgroup_hash': 251, 'subgroup_order': 432, 'subgroup_tex': '(C_3\\times A_4):C_{12}', 'supersolvable': False, 'sylow': 0}
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id: 186248044
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 144, 'counter': 388, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.555', 'subgroup_hash': 555, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:A_4', 'supersolvable': False, 'sylow': 0}
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id: 186248045
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 48, 'counter': 389, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.555', 'subgroup_hash': 555, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:A_4', 'supersolvable': False, 'sylow': 0}
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id: 186248047
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 48, 'counter': 390, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.750', 'subgroup_hash': 750, 'subgroup_order': 432, 'subgroup_tex': 'C_3\\times A_4^2', 'supersolvable': False, 'sylow': 0}
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id: 186248048
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 144, 'counter': 391, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.750', 'subgroup_hash': 750, 'subgroup_order': 432, 'subgroup_tex': 'C_3\\times A_4^2', 'supersolvable': False, 'sylow': 0}
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id: 186248049
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 144, 'counter': 392, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.526', 'subgroup_hash': 526, 'subgroup_order': 432, 'subgroup_tex': 'C_3.A_4^2', 'supersolvable': False, 'sylow': 0}
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id: 186248050
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 48, 'counter': 393, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.526', 'subgroup_hash': 526, 'subgroup_order': 432, 'subgroup_tex': 'C_3.A_4^2', 'supersolvable': False, 'sylow': 0}
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id: 186248051
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 144, 'counter': 394, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.770', 'subgroup_hash': 770, 'subgroup_order': 432, 'subgroup_tex': 'A_4\\times C_6^2', 'supersolvable': False, 'sylow': 0}
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id: 186248052
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 144, 'counter': 395, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.770', 'subgroup_hash': 770, 'subgroup_order': 432, 'subgroup_tex': 'A_4\\times C_6^2', 'supersolvable': False, 'sylow': 0}
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id: 186248053
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 144, 'counter': 396, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.771', 'subgroup_hash': 771, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:A_4', 'supersolvable': False, 'sylow': 0}
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id: 186248054
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 16, 'counter': 397, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.550', 'subgroup_hash': 550, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:A_4', 'supersolvable': False, 'sylow': 0}
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id: 186248055
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 16, 'counter': 398, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.550', 'subgroup_hash': 550, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:A_4', 'supersolvable': False, 'sylow': 0}
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id: 186248056
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 16, 'counter': 399, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.750', 'subgroup_hash': 750, 'subgroup_order': 432, 'subgroup_tex': 'C_3\\times A_4^2', 'supersolvable': False, 'sylow': 0}
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id: 186248059
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 16, 'counter': 400, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.526', 'subgroup_hash': 526, 'subgroup_order': 432, 'subgroup_tex': 'C_3.A_4^2', 'supersolvable': False, 'sylow': 0}
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id: 186248060
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 16, 'counter': 401, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.750', 'subgroup_hash': 750, 'subgroup_order': 432, 'subgroup_tex': 'C_3\\times A_4^2', 'supersolvable': False, 'sylow': 0}
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id: 186248061
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 16, 'counter': 402, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.526', 'subgroup_hash': 526, 'subgroup_order': 432, 'subgroup_tex': 'C_3.A_4^2', 'supersolvable': False, 'sylow': 0}
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id: 186248062
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 403, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.601', 'subgroup_hash': 601, 'subgroup_order': 432, 'subgroup_tex': 'D_6:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248063
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 404, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.595', 'subgroup_hash': 595, 'subgroup_order': 432, 'subgroup_tex': 'C_2.S_3^3', 'supersolvable': True, 'sylow': 0}
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id: 186248064
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 405, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.759', 'subgroup_hash': 759, 'subgroup_order': 432, 'subgroup_tex': 'C_2\\times S_3^3', 'supersolvable': True, 'sylow': 0}
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id: 186248065
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 406, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.601', 'subgroup_hash': 601, 'subgroup_order': 432, 'subgroup_tex': 'D_6:S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186248066
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 407, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.595', 'subgroup_hash': 595, 'subgroup_order': 432, 'subgroup_tex': 'C_2.S_3^3', 'supersolvable': True, 'sylow': 0}
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id: 186248067
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 408, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.605', 'subgroup_hash': 605, 'subgroup_order': 432, 'subgroup_tex': 'C_2.S_3^3', 'supersolvable': True, 'sylow': 0}
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id: 186248068
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 409, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.598', 'subgroup_hash': 598, 'subgroup_order': 432, 'subgroup_tex': 'D_6:S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186248070
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 410, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.609', 'subgroup_hash': 609, 'subgroup_order': 432, 'subgroup_tex': 'C_2.S_3^3', 'supersolvable': True, 'sylow': 0}
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id: 186248071
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 411, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.598', 'subgroup_hash': 598, 'subgroup_order': 432, 'subgroup_tex': 'D_6:S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186248072
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 412, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.602', 'subgroup_hash': 602, 'subgroup_order': 432, 'subgroup_tex': 'D_6:S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186248073
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 413, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.606', 'subgroup_hash': 606, 'subgroup_order': 432, 'subgroup_tex': 'C_2.S_3^3', 'supersolvable': True, 'sylow': 0}
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id: 186248074
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 414, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.609', 'subgroup_hash': 609, 'subgroup_order': 432, 'subgroup_tex': 'C_2.S_3^3', 'supersolvable': True, 'sylow': 0}
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id: 186248075
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 415, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.599', 'subgroup_hash': 599, 'subgroup_order': 432, 'subgroup_tex': 'D_6:S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186248076
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 416, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.598', 'subgroup_hash': 598, 'subgroup_order': 432, 'subgroup_tex': 'D_6:S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186248077
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 417, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.599', 'subgroup_hash': 599, 'subgroup_order': 432, 'subgroup_tex': 'D_6:S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186248078
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 418, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.606', 'subgroup_hash': 606, 'subgroup_order': 432, 'subgroup_tex': 'C_2.S_3^3', 'supersolvable': True, 'sylow': 0}
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id: 186248079
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 419, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.609', 'subgroup_hash': 609, 'subgroup_order': 432, 'subgroup_tex': 'C_2.S_3^3', 'supersolvable': True, 'sylow': 0}
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id: 186248081
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 420, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.612', 'subgroup_hash': 612, 'subgroup_order': 432, 'subgroup_tex': 'C_2.S_3^3', 'supersolvable': True, 'sylow': 0}
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id: 186248082
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 421, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.602', 'subgroup_hash': 602, 'subgroup_order': 432, 'subgroup_tex': 'D_6:S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186248083
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 422, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.612', 'subgroup_hash': 612, 'subgroup_order': 432, 'subgroup_tex': 'C_2.S_3^3', 'supersolvable': True, 'sylow': 0}
-
id: 186248084
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 423, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.542', 'subgroup_hash': 542, 'subgroup_order': 432, 'subgroup_tex': 'C_2\\times C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
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id: 186248085
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 424, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.749', 'subgroup_hash': 749, 'subgroup_order': 432, 'subgroup_tex': 'A_4\\times S_3^2', 'supersolvable': False, 'sylow': 0}
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id: 186248086
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 425, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.523', 'subgroup_hash': 523, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
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id: 186248087
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 426, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.523', 'subgroup_hash': 523, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
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id: 186248088
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 427, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.748', 'subgroup_hash': 748, 'subgroup_order': 432, 'subgroup_tex': 'A_4:S_3^2', 'supersolvable': False, 'sylow': 0}
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id: 186248089
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 428, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.746', 'subgroup_hash': 746, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
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id: 186248090
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 429, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.523', 'subgroup_hash': 523, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
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id: 186248092
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 430, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.686', 'subgroup_hash': 686, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186248093
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 431, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.768', 'subgroup_hash': 768, 'subgroup_order': 432, 'subgroup_tex': 'C_3:D_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186248094
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 432, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.686', 'subgroup_hash': 686, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186248095
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 433, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.ek1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.679', 'subgroup_hash': 679, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
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id: 186248096
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 434, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.el1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.538', 'subgroup_hash': 538, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
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id: 186248097
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 435, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.em1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.686', 'subgroup_hash': 686, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186248098
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 436, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.en1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.659', 'subgroup_hash': 659, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186248099
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 437, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.eo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.653', 'subgroup_hash': 653, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
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id: 186248100
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 438, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.ep1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.652', 'subgroup_hash': 652, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
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id: 186248101
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 439, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.eq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.658', 'subgroup_hash': 658, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186248103
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 440, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.er1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.745', 'subgroup_hash': 745, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
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id: 186248104
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 441, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.es1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.745', 'subgroup_hash': 745, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
-
id: 186248105
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 442, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.et1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.681', 'subgroup_hash': 681, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186248106
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 443, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.eu1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.eu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.745', 'subgroup_hash': 745, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
-
id: 186248107
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 444, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.ev1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ev1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.523', 'subgroup_hash': 523, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
-
id: 186248108
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 445, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.ew1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ew1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.658', 'subgroup_hash': 658, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186248109
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 446, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.ex1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ex1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.535', 'subgroup_hash': 535, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
-
id: 186248110
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 447, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.ey1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ey1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.747', 'subgroup_hash': 747, 'subgroup_order': 432, 'subgroup_tex': 'A_4:S_3^2', 'supersolvable': False, 'sylow': 0}
-
id: 186248111
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 448, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.ez1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ez1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.652', 'subgroup_hash': 652, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186248112
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 449, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.fa1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.693', 'subgroup_hash': 693, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186248114
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 450, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.fb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.747', 'subgroup_hash': 747, 'subgroup_order': 432, 'subgroup_tex': 'A_4:S_3^2', 'supersolvable': False, 'sylow': 0}
-
id: 186248115
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 451, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.fc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.682', 'subgroup_hash': 682, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
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id: 186248116
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 452, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.fd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.523', 'subgroup_hash': 523, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
-
id: 186248117
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 453, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.fe1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.523', 'subgroup_hash': 523, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
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id: 186248118
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 454, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.ff1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ff1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.696', 'subgroup_hash': 696, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186248119
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 455, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.fg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.686', 'subgroup_hash': 686, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186248120
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 456, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.72.fh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.451', 'subgroup_hash': 451, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
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id: 186248121
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 457, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.81.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '81.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 81, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.17948', 'subgroup_hash': 17948, 'subgroup_order': 384, 'subgroup_tex': 'C_2^4:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248122
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 458, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.81.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '81.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 81, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.12882', 'subgroup_hash': 12882, 'subgroup_order': 384, 'subgroup_tex': 'C_2\\wr C_2^2\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186248123
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 459, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.81.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '81.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 81, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.12882', 'subgroup_hash': 12882, 'subgroup_order': 384, 'subgroup_tex': 'C_2\\wr C_2^2\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186248125
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 460, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.96.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.144', 'subgroup_hash': 144, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186248126
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 27, 'counter': 461, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.96.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.145', 'subgroup_hash': 145, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186248127
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 462, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.96.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.144', 'subgroup_hash': 144, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186248128
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 463, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.96.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.144', 'subgroup_hash': 144, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186248129
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 27, 'counter': 464, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.96.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.99', 'subgroup_hash': 99, 'subgroup_order': 324, 'subgroup_tex': '\\He_3:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186248130
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 465, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.96.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.98', 'subgroup_hash': 98, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186248131
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 466, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.96.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.152', 'subgroup_hash': 152, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:C_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248132
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 467, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.96.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.135', 'subgroup_hash': 135, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:A_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248133
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 468, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.96.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.135', 'subgroup_hash': 135, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:A_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248134
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 469, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.96.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.135', 'subgroup_hash': 135, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:A_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248136
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 470, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.96.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.135', 'subgroup_hash': 135, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:A_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248137
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 471, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.96.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.171', 'subgroup_hash': 171, 'subgroup_order': 324, 'subgroup_tex': 'A_4\\times C_3^3', 'supersolvable': False, 'sylow': 0}
-
id: 186248138
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 472, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.96.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.135', 'subgroup_hash': 135, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:A_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248139
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 473, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.96.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.135', 'subgroup_hash': 135, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:A_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248140
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 474, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.96.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.167', 'subgroup_hash': 167, 'subgroup_order': 324, 'subgroup_tex': 'C_3\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248141
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 475, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.96.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.169', 'subgroup_hash': 169, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248142
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 476, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.96.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.116', 'subgroup_hash': 116, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248143
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 477, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.96.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.121', 'subgroup_hash': 121, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248144
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 478, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.96.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.124', 'subgroup_hash': 124, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248145
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 479, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.96.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.124', 'subgroup_hash': 124, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248147
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 480, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.96.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.122', 'subgroup_hash': 122, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248148
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 481, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.96.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.117', 'subgroup_hash': 117, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186248149
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 482, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.96.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.167', 'subgroup_hash': 167, 'subgroup_order': 324, 'subgroup_tex': 'C_3\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248150
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 483, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.96.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.117', 'subgroup_hash': 117, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186248151
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 484, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.96.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.116', 'subgroup_hash': 116, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248152
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 485, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.96.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.169', 'subgroup_hash': 169, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248153
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 486, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.96.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.169', 'subgroup_hash': 169, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248154
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 487, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.96.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.121', 'subgroup_hash': 121, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248155
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 488, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.96.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.124', 'subgroup_hash': 124, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248156
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 288, 'counter': 489, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '31104.fx.108.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '108.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '108.17', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 17, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 108, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2:D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '288.1036', 'subgroup_hash': 1036, 'subgroup_order': 288, 'subgroup_tex': '(C_2\\times C_6):S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248158
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 490, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.958', 'subgroup_hash': 958, 'subgroup_order': 288, 'subgroup_tex': 'D_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248159
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 491, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.960', 'subgroup_hash': 960, 'subgroup_order': 288, 'subgroup_tex': 'D_4:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248160
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 492, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.977', 'subgroup_hash': 977, 'subgroup_order': 288, 'subgroup_tex': 'D_6^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 186248161
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 493, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.954', 'subgroup_hash': 954, 'subgroup_order': 288, 'subgroup_tex': 'D_{12}:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186248162
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 494, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.962', 'subgroup_hash': 962, 'subgroup_order': 288, 'subgroup_tex': 'D_{12}:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186248163
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 495, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.962', 'subgroup_hash': 962, 'subgroup_order': 288, 'subgroup_tex': 'D_{12}:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186248164
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 496, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.978', 'subgroup_hash': 978, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248165
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 497, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.956', 'subgroup_hash': 956, 'subgroup_order': 288, 'subgroup_tex': 'D_{12}:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186248166
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 498, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1007', 'subgroup_hash': 1007, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 186248167
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 499, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.977', 'subgroup_hash': 977, 'subgroup_order': 288, 'subgroup_tex': 'D_6^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 186248170
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 500, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.977', 'subgroup_hash': 977, 'subgroup_order': 288, 'subgroup_tex': 'D_6^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 186248171
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 501, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.977', 'subgroup_hash': 977, 'subgroup_order': 288, 'subgroup_tex': 'D_6^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 186248172
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 502, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1007', 'subgroup_hash': 1007, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 186248173
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 503, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.977', 'subgroup_hash': 977, 'subgroup_order': 288, 'subgroup_tex': 'D_6^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 186248174
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 504, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.977', 'subgroup_hash': 977, 'subgroup_order': 288, 'subgroup_tex': 'D_6^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 186248175
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 505, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.737', 'subgroup_hash': 737, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 186248176
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 506, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.622', 'subgroup_hash': 622, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3.S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248177
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 507, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.622', 'subgroup_hash': 622, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3.S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248178
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 508, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.622', 'subgroup_hash': 622, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3.S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248179
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 509, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.622', 'subgroup_hash': 622, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3.S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248181
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 510, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.737', 'subgroup_hash': 737, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 186248182
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 511, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.622', 'subgroup_hash': 622, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3.S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248183
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 512, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.994', 'subgroup_hash': 994, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 186248184
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 513, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.794', 'subgroup_hash': 794, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186248185
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 514, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.268', 'subgroup_hash': 268, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186248186
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 515, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.268', 'subgroup_hash': 268, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186248187
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 516, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.994', 'subgroup_hash': 994, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 186248188
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 517, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.978', 'subgroup_hash': 978, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248189
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 518, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.629', 'subgroup_hash': 629, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186248190
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 519, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.629', 'subgroup_hash': 629, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186248192
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 520, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.629', 'subgroup_hash': 629, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186248193
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 521, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.228', 'subgroup_hash': 228, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186248194
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 522, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.240', 'subgroup_hash': 240, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186248195
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 523, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.240', 'subgroup_hash': 240, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186248196
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 524, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.228', 'subgroup_hash': 228, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186248197
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 525, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.994', 'subgroup_hash': 994, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 186248198
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 526, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.978', 'subgroup_hash': 978, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248199
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 527, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.629', 'subgroup_hash': 629, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186248200
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 528, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.629', 'subgroup_hash': 629, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186248201
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 529, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.629', 'subgroup_hash': 629, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186248203
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 530, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.240', 'subgroup_hash': 240, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186248204
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 531, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.228', 'subgroup_hash': 228, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186248205
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 532, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.240', 'subgroup_hash': 240, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186248206
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 533, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.228', 'subgroup_hash': 228, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186248207
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 534, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.978', 'subgroup_hash': 978, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248208
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 535, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.739', 'subgroup_hash': 739, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186248209
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 536, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.229', 'subgroup_hash': 229, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186248210
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 537, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.229', 'subgroup_hash': 229, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': True, 'sylow': 0}
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id: 186248211
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 538, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.978', 'subgroup_hash': 978, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3:S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186248212
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 539, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.794', 'subgroup_hash': 794, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186248214
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 540, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.268', 'subgroup_hash': 268, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': True, 'sylow': 0}
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id: 186248215
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 541, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.629', 'subgroup_hash': 629, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186248216
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 542, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.629', 'subgroup_hash': 629, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186248217
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 543, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.240', 'subgroup_hash': 240, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': True, 'sylow': 0}
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id: 186248218
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 544, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.228', 'subgroup_hash': 228, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': True, 'sylow': 0}
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id: 186248219
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 545, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.629', 'subgroup_hash': 629, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186248220
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 546, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.629', 'subgroup_hash': 629, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186248221
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 547, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.739', 'subgroup_hash': 739, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186248222
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 548, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.240', 'subgroup_hash': 240, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': True, 'sylow': 0}
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id: 186248223
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 549, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.228', 'subgroup_hash': 228, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': True, 'sylow': 0}
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id: 186248225
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 550, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.229', 'subgroup_hash': 229, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': True, 'sylow': 0}
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id: 186248226
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 551, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.229', 'subgroup_hash': 229, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': True, 'sylow': 0}
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id: 186248227
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 552, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
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id: 186248228
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 553, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248229
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 554, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248230
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 555, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.856', 'subgroup_hash': 856, 'subgroup_order': 288, 'subgroup_tex': 'D_6.S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248231
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 556, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.856', 'subgroup_hash': 856, 'subgroup_order': 288, 'subgroup_tex': 'D_6.S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248232
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 557, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.856', 'subgroup_hash': 856, 'subgroup_order': 288, 'subgroup_tex': 'D_6.S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248233
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 558, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1007', 'subgroup_hash': 1007, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 186248234
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 559, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.977', 'subgroup_hash': 977, 'subgroup_order': 288, 'subgroup_tex': 'D_6^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 186248236
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 560, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.977', 'subgroup_hash': 977, 'subgroup_order': 288, 'subgroup_tex': 'D_6^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 186248237
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 561, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.977', 'subgroup_hash': 977, 'subgroup_order': 288, 'subgroup_tex': 'D_6^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 186248238
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 562, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.622', 'subgroup_hash': 622, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3.S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248239
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 563, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.737', 'subgroup_hash': 737, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 186248240
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 564, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.622', 'subgroup_hash': 622, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3.S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248241
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 565, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.622', 'subgroup_hash': 622, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3.S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248242
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 566, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.794', 'subgroup_hash': 794, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186248243
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 567, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.857', 'subgroup_hash': 857, 'subgroup_order': 288, 'subgroup_tex': 'D_6:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248244
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 568, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.857', 'subgroup_hash': 857, 'subgroup_order': 288, 'subgroup_tex': 'D_6:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248245
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 569, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.857', 'subgroup_hash': 857, 'subgroup_order': 288, 'subgroup_tex': 'D_6:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248247
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 570, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.629', 'subgroup_hash': 629, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186248248
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 571, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.629', 'subgroup_hash': 629, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186248249
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 572, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.629', 'subgroup_hash': 629, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186248250
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 573, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.858', 'subgroup_hash': 858, 'subgroup_order': 288, 'subgroup_tex': 'D_6:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248251
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 574, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.858', 'subgroup_hash': 858, 'subgroup_order': 288, 'subgroup_tex': 'D_6:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248252
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 575, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.858', 'subgroup_hash': 858, 'subgroup_order': 288, 'subgroup_tex': 'D_6:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248253
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 576, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.629', 'subgroup_hash': 629, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186248254
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 577, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.629', 'subgroup_hash': 629, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186248255
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 578, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.629', 'subgroup_hash': 629, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186248256
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 579, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.739', 'subgroup_hash': 739, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186248258
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 580, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1029', 'subgroup_hash': 1029, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times A_4^2', 'supersolvable': False, 'sylow': 0}
-
id: 186248259
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 581, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1037', 'subgroup_hash': 1037, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
-
id: 186248260
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 48, 'counter': 582, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1038', 'subgroup_hash': 1038, 'subgroup_order': 288, 'subgroup_tex': 'S_3\\times C_2^2:A_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248261
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 144, 'counter': 583, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1038', 'subgroup_hash': 1038, 'subgroup_order': 288, 'subgroup_tex': 'S_3\\times C_2^2:A_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248262
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 584, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1037', 'subgroup_hash': 1037, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
-
id: 186248263
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 585, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1037', 'subgroup_hash': 1037, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
-
id: 186248264
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 586, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1038', 'subgroup_hash': 1038, 'subgroup_order': 288, 'subgroup_tex': 'S_3\\times C_2^2:A_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248265
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 48, 'counter': 587, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1044', 'subgroup_hash': 1044, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 186248266
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 144, 'counter': 588, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1044', 'subgroup_hash': 1044, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 186248267
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 589, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1044', 'subgroup_hash': 1044, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 186248269
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 48, 'counter': 590, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.817', 'subgroup_hash': 817, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186248270
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 144, 'counter': 591, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.634', 'subgroup_hash': 634, 'subgroup_order': 288, 'subgroup_tex': 'C_3\\times C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248271
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 48, 'counter': 592, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.634', 'subgroup_hash': 634, 'subgroup_order': 288, 'subgroup_tex': 'C_3\\times C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248272
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 48, 'counter': 593, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.724', 'subgroup_hash': 724, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186248273
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 48, 'counter': 594, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1035', 'subgroup_hash': 1035, 'subgroup_order': 288, 'subgroup_tex': 'C_3\\times C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248274
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 48, 'counter': 595, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.411', 'subgroup_hash': 411, 'subgroup_order': 288, 'subgroup_tex': '(C_2\\times D_6):A_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248275
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 48, 'counter': 596, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.411', 'subgroup_hash': 411, 'subgroup_order': 288, 'subgroup_tex': '(C_2\\times D_6):A_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248276
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 144, 'counter': 597, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.724', 'subgroup_hash': 724, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186248277
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 16, 'counter': 598, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1025', 'subgroup_hash': 1025, 'subgroup_order': 288, 'subgroup_tex': 'A_4\\wr C_2', 'supersolvable': False, 'sylow': 0}
-
id: 186248278
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 16, 'counter': 599, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1025', 'subgroup_hash': 1025, 'subgroup_order': 288, 'subgroup_tex': 'A_4\\wr C_2', 'supersolvable': False, 'sylow': 0}
-
id: 186248281
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 48, 'counter': 600, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.634', 'subgroup_hash': 634, 'subgroup_order': 288, 'subgroup_tex': 'C_3\\times C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248282
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 48, 'counter': 601, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.724', 'subgroup_hash': 724, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186248283
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 144, 'counter': 602, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1035', 'subgroup_hash': 1035, 'subgroup_order': 288, 'subgroup_tex': 'C_3\\times C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248284
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 144, 'counter': 603, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.ek1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.411', 'subgroup_hash': 411, 'subgroup_order': 288, 'subgroup_tex': '(C_2\\times D_6):A_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248285
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 48, 'counter': 604, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.el1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1035', 'subgroup_hash': 1035, 'subgroup_order': 288, 'subgroup_tex': 'C_3\\times C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248286
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 48, 'counter': 605, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.em1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.411', 'subgroup_hash': 411, 'subgroup_order': 288, 'subgroup_tex': '(C_2\\times D_6):A_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248287
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 48, 'counter': 606, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.en1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1035', 'subgroup_hash': 1035, 'subgroup_order': 288, 'subgroup_tex': 'C_3\\times C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248288
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 144, 'counter': 607, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.eo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.724', 'subgroup_hash': 724, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186248289
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 16, 'counter': 608, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.ep1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1025', 'subgroup_hash': 1025, 'subgroup_order': 288, 'subgroup_tex': 'A_4\\wr C_2', 'supersolvable': False, 'sylow': 0}
-
id: 186248290
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 16, 'counter': 609, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.eq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1025', 'subgroup_hash': 1025, 'subgroup_order': 288, 'subgroup_tex': 'A_4\\wr C_2', 'supersolvable': False, 'sylow': 0}
-
id: 186248292
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 16, 'counter': 610, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.er1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1025', 'subgroup_hash': 1025, 'subgroup_order': 288, 'subgroup_tex': 'A_4\\wr C_2', 'supersolvable': False, 'sylow': 0}
-
id: 186248293
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 16, 'counter': 611, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.es1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1025', 'subgroup_hash': 1025, 'subgroup_order': 288, 'subgroup_tex': 'A_4\\wr C_2', 'supersolvable': False, 'sylow': 0}
-
id: 186248294
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 16, 'counter': 612, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.et1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1025', 'subgroup_hash': 1025, 'subgroup_order': 288, 'subgroup_tex': 'A_4\\wr C_2', 'supersolvable': False, 'sylow': 0}
-
id: 186248295
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 48, 'counter': 613, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.eu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.eu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.810', 'subgroup_hash': 810, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186248296
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 48, 'counter': 614, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.ev1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ev1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1036', 'subgroup_hash': 1036, 'subgroup_order': 288, 'subgroup_tex': '(C_2\\times C_6):S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248297
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 48, 'counter': 615, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.ew1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ew1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1036', 'subgroup_hash': 1036, 'subgroup_order': 288, 'subgroup_tex': '(C_2\\times C_6):S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248298
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 144, 'counter': 616, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.ex1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.ex1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.817', 'subgroup_hash': 817, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186248299
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 48, 'counter': 617, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.ey1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ey1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.724', 'subgroup_hash': 724, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186248300
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 48, 'counter': 618, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.ez1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ez1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.906', 'subgroup_hash': 906, 'subgroup_order': 288, 'subgroup_tex': 'C_3\\times \\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
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id: 186248301
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 48, 'counter': 619, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.fa1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.fa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1035', 'subgroup_hash': 1035, 'subgroup_order': 288, 'subgroup_tex': 'C_3\\times C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248303
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 144, 'counter': 620, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.fb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.fb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1035', 'subgroup_hash': 1035, 'subgroup_order': 288, 'subgroup_tex': 'C_3\\times C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248304
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 48, 'counter': 621, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.fc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.fc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.906', 'subgroup_hash': 906, 'subgroup_order': 288, 'subgroup_tex': 'C_3\\times \\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
-
id: 186248305
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 48, 'counter': 622, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.fd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.fd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1035', 'subgroup_hash': 1035, 'subgroup_order': 288, 'subgroup_tex': 'C_3\\times C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248306
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 48, 'counter': 623, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.fd2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.fd2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1035', 'subgroup_hash': 1035, 'subgroup_order': 288, 'subgroup_tex': 'C_3\\times C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248307
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 16, 'counter': 624, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.fe1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.fe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.724', 'subgroup_hash': 724, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186248308
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 16, 'counter': 625, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.ff1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ff1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.906', 'subgroup_hash': 906, 'subgroup_order': 288, 'subgroup_tex': 'C_3\\times \\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
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id: 186248309
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 16, 'counter': 626, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.fg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.fg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.906', 'subgroup_hash': 906, 'subgroup_order': 288, 'subgroup_tex': 'C_3\\times \\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
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id: 186248310
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 16, 'counter': 627, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.fh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.fh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1035', 'subgroup_hash': 1035, 'subgroup_order': 288, 'subgroup_tex': 'C_3\\times C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186248311
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 16, 'counter': 628, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.fi1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.fi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.906', 'subgroup_hash': 906, 'subgroup_order': 288, 'subgroup_tex': 'C_3\\times \\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
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id: 186248312
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 16, 'counter': 629, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.fi2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.fi2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.906', 'subgroup_hash': 906, 'subgroup_order': 288, 'subgroup_tex': 'C_3\\times \\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
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id: 186248314
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 16, 'counter': 630, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.fj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.fj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1035', 'subgroup_hash': 1035, 'subgroup_order': 288, 'subgroup_tex': 'C_3\\times C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248315
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 16, 'counter': 631, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.fk1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.fk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1026', 'subgroup_hash': 1026, 'subgroup_order': 288, 'subgroup_tex': '\\PSOPlus(4,3)', 'supersolvable': False, 'sylow': 0}
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id: 186248316
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 48, 'counter': 632, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.fl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.fl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.724', 'subgroup_hash': 724, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186248317
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 16, 'counter': 633, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.fm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.fm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.724', 'subgroup_hash': 724, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186248318
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 634, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.fn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.fn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.917', 'subgroup_hash': 917, 'subgroup_order': 288, 'subgroup_tex': 'C_3:\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
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id: 186248319
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 48, 'counter': 635, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.fo1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.fo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1036', 'subgroup_hash': 1036, 'subgroup_order': 288, 'subgroup_tex': '(C_2\\times C_6):S_4', 'supersolvable': False, 'sylow': 0}
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id: 186248320
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 144, 'counter': 636, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.fp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.fp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1036', 'subgroup_hash': 1036, 'subgroup_order': 288, 'subgroup_tex': '(C_2\\times C_6):S_4', 'supersolvable': False, 'sylow': 0}
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id: 186248321
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 48, 'counter': 637, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.fq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.fq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1036', 'subgroup_hash': 1036, 'subgroup_order': 288, 'subgroup_tex': '(C_2\\times C_6):S_4', 'supersolvable': False, 'sylow': 0}
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id: 186248322
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 144, 'counter': 638, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.fr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.fr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.810', 'subgroup_hash': 810, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186248323
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 639, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.fs1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.fs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.917', 'subgroup_hash': 917, 'subgroup_order': 288, 'subgroup_tex': 'C_3:\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
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id: 186248325
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 640, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.ft1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ft1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.917', 'subgroup_hash': 917, 'subgroup_order': 288, 'subgroup_tex': 'C_3:\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
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id: 186248326
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 641, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.fu1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.fu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1036', 'subgroup_hash': 1036, 'subgroup_order': 288, 'subgroup_tex': '(C_2\\times C_6):S_4', 'supersolvable': False, 'sylow': 0}
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id: 186248327
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 642, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.fv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.fv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.917', 'subgroup_hash': 917, 'subgroup_order': 288, 'subgroup_tex': 'C_3:\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
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id: 186248328
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 643, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.fw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.fw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1026', 'subgroup_hash': 1026, 'subgroup_order': 288, 'subgroup_tex': '\\PSOPlus(4,3)', 'supersolvable': False, 'sylow': 0}
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id: 186248329
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 644, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.fx1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.fx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1026', 'subgroup_hash': 1026, 'subgroup_order': 288, 'subgroup_tex': '\\PSOPlus(4,3)', 'supersolvable': False, 'sylow': 0}
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id: 186248330
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 645, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.fy1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.fy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1026', 'subgroup_hash': 1026, 'subgroup_order': 288, 'subgroup_tex': '\\PSOPlus(4,3)', 'supersolvable': False, 'sylow': 0}
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id: 186248331
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 646, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.fz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.fz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1026', 'subgroup_hash': 1026, 'subgroup_order': 288, 'subgroup_tex': '\\PSOPlus(4,3)', 'supersolvable': False, 'sylow': 0}
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id: 186248332
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 647, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.ga1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ga1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1026', 'subgroup_hash': 1026, 'subgroup_order': 288, 'subgroup_tex': '\\PSOPlus(4,3)', 'supersolvable': False, 'sylow': 0}
-
id: 186248333
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 648, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.gb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.gb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1026', 'subgroup_hash': 1026, 'subgroup_order': 288, 'subgroup_tex': '\\PSOPlus(4,3)', 'supersolvable': False, 'sylow': 0}
-
id: 186248334
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 649, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.gc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.gc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1026', 'subgroup_hash': 1026, 'subgroup_order': 288, 'subgroup_tex': '\\PSOPlus(4,3)', 'supersolvable': False, 'sylow': 0}
-
id: 186248336
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 650, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.gc2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.gc2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1026', 'subgroup_hash': 1026, 'subgroup_order': 288, 'subgroup_tex': '\\PSOPlus(4,3)', 'supersolvable': False, 'sylow': 0}
-
id: 186248337
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 651, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.gd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.gd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248338
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 652, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.ge1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ge1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248339
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 653, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.gf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.gf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.960', 'subgroup_hash': 960, 'subgroup_order': 288, 'subgroup_tex': 'D_4:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248340
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 654, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.gg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.gg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.960', 'subgroup_hash': 960, 'subgroup_order': 288, 'subgroup_tex': 'D_4:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248341
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 655, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.gh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.gh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.954', 'subgroup_hash': 954, 'subgroup_order': 288, 'subgroup_tex': 'D_{12}:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186248342
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 656, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.gi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.gi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.977', 'subgroup_hash': 977, 'subgroup_order': 288, 'subgroup_tex': 'D_6^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 186248343
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 657, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.gj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.gj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.958', 'subgroup_hash': 958, 'subgroup_order': 288, 'subgroup_tex': 'D_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248344
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 658, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.gk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.gk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.958', 'subgroup_hash': 958, 'subgroup_order': 288, 'subgroup_tex': 'D_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248345
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 659, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.gl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.gl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.962', 'subgroup_hash': 962, 'subgroup_order': 288, 'subgroup_tex': 'D_{12}:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186248347
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 660, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.gm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.gm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.962', 'subgroup_hash': 962, 'subgroup_order': 288, 'subgroup_tex': 'D_{12}:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186248348
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 661, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.gn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.gn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.956', 'subgroup_hash': 956, 'subgroup_order': 288, 'subgroup_tex': 'D_{12}:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186248349
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 662, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.go1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.go1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.978', 'subgroup_hash': 978, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248350
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 663, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.gp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.gp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.962', 'subgroup_hash': 962, 'subgroup_order': 288, 'subgroup_tex': 'D_{12}:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186248351
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 664, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.108.gq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.gq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.962', 'subgroup_hash': 962, 'subgroup_order': 288, 'subgroup_tex': 'D_{12}:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186248352
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 665, 'cyclic': False, 'direct': None, 'hall': 3, 'label': '31104.fx.128.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.37', 'subgroup_hash': 37, 'subgroup_order': 243, 'subgroup_tex': 'C_3^4:C_3', 'supersolvable': True, 'sylow': 3}
-
id: 186248353
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 54, 'counter': 666, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.176', 'subgroup_hash': 176, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186248354
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 667, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.139', 'subgroup_hash': 139, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': True, 'sylow': 0}
-
id: 186248355
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 668, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.176', 'subgroup_hash': 176, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186248356
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 669, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.176', 'subgroup_hash': 176, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186248358
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 670, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.144', 'subgroup_hash': 144, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': True, 'sylow': 0}
-
id: 186248359
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 671, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248360
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 672, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.102', 'subgroup_hash': 102, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248361
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 673, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.125', 'subgroup_hash': 125, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248362
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 674, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.34', 'subgroup_hash': 34, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248363
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 675, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248364
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 676, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.126', 'subgroup_hash': 126, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248365
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 677, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.127', 'subgroup_hash': 127, 'subgroup_order': 216, 'subgroup_tex': 'C_3^3:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186248366
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 678, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248367
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 679, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.128', 'subgroup_hash': 128, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186248369
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 680, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.128', 'subgroup_hash': 128, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186248370
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 681, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.37', 'subgroup_hash': 37, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186248371
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 682, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.35', 'subgroup_hash': 35, 'subgroup_order': 216, 'subgroup_tex': '\\He_3:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186248372
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 683, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.129', 'subgroup_hash': 129, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186248373
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 684, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.126', 'subgroup_hash': 126, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248374
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 685, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.129', 'subgroup_hash': 129, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186248375
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 686, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.129', 'subgroup_hash': 129, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186248376
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 54, 'counter': 687, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.176', 'subgroup_hash': 176, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186248377
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 688, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.139', 'subgroup_hash': 139, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': True, 'sylow': 0}
-
id: 186248378
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 689, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.144', 'subgroup_hash': 144, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': True, 'sylow': 0}
-
id: 186248380
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 690, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.174', 'subgroup_hash': 174, 'subgroup_order': 216, 'subgroup_tex': 'S_3\\times C_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248381
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 691, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.176', 'subgroup_hash': 176, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186248382
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 692, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.176', 'subgroup_hash': 176, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186248383
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 693, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.175', 'subgroup_hash': 175, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': True, 'sylow': 0}
-
id: 186248384
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 694, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.138', 'subgroup_hash': 138, 'subgroup_order': 216, 'subgroup_tex': 'C_6.C_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248385
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 695, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.138', 'subgroup_hash': 138, 'subgroup_order': 216, 'subgroup_tex': 'C_6.C_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248386
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 696, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.143', 'subgroup_hash': 143, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2.C_6', 'supersolvable': True, 'sylow': 0}
-
id: 186248387
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 697, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.143', 'subgroup_hash': 143, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2.C_6', 'supersolvable': True, 'sylow': 0}
-
id: 186248388
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 27, 'counter': 698, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.177', 'subgroup_hash': 177, 'subgroup_order': 216, 'subgroup_tex': 'C_6^3', 'supersolvable': True, 'sylow': 0}
-
id: 186248389
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 699, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.166', 'subgroup_hash': 166, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
-
id: 186248392
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 700, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.166', 'subgroup_hash': 166, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
-
id: 186248393
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 701, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.166', 'subgroup_hash': 166, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
-
id: 186248394
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 702, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.99', 'subgroup_hash': 99, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
-
id: 186248395
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 703, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.175', 'subgroup_hash': 175, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': True, 'sylow': 0}
-
id: 186248396
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 704, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.167', 'subgroup_hash': 167, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
-
id: 186248397
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 705, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.167', 'subgroup_hash': 167, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
-
id: 186248398
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 706, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.110', 'subgroup_hash': 110, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': True, 'sylow': 0}
-
id: 186248399
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 707, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.99', 'subgroup_hash': 99, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
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id: 186248400
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 54, 'counter': 708, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.176', 'subgroup_hash': 176, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186248401
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 709, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.139', 'subgroup_hash': 139, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': True, 'sylow': 0}
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id: 186248403
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 710, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.139', 'subgroup_hash': 139, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': True, 'sylow': 0}
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id: 186248404
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 711, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.163', 'subgroup_hash': 163, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2\\times S_4', 'supersolvable': False, 'sylow': 0}
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id: 186248405
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 712, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.163', 'subgroup_hash': 163, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2\\times S_4', 'supersolvable': False, 'sylow': 0}
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id: 186248406
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 713, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.139', 'subgroup_hash': 139, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': True, 'sylow': 0}
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id: 186248407
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 714, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.163', 'subgroup_hash': 163, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2\\times S_4', 'supersolvable': False, 'sylow': 0}
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id: 186248408
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 715, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.163', 'subgroup_hash': 163, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2\\times S_4', 'supersolvable': False, 'sylow': 0}
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id: 186248409
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 716, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.95', 'subgroup_hash': 95, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186248410
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 717, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.164', 'subgroup_hash': 164, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186248411
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 718, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.95', 'subgroup_hash': 95, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186248412
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 719, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.72', 'subgroup_hash': 72, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186248414
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 720, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.95', 'subgroup_hash': 95, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186248415
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 721, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.95', 'subgroup_hash': 95, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186248416
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 722, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.164', 'subgroup_hash': 164, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186248417
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 723, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.95', 'subgroup_hash': 95, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186248418
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 724, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.164', 'subgroup_hash': 164, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186248419
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 725, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.167', 'subgroup_hash': 167, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
-
id: 186248420
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 726, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.99', 'subgroup_hash': 99, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
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id: 186248421
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 727, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.ci2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ci2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.99', 'subgroup_hash': 99, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
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id: 186248422
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 728, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.176', 'subgroup_hash': 176, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186248423
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 729, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.92', 'subgroup_hash': 92, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186248425
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 730, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.92', 'subgroup_hash': 92, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186248426
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 731, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.144', 'subgroup_hash': 144, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': True, 'sylow': 0}
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id: 186248427
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 732, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.60', 'subgroup_hash': 60, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': True, 'sylow': 0}
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id: 186248428
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 733, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.92', 'subgroup_hash': 92, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186248429
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 734, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.60', 'subgroup_hash': 60, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': True, 'sylow': 0}
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id: 186248430
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 735, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.92', 'subgroup_hash': 92, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186248431
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 736, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.165', 'subgroup_hash': 165, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186248432
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 737, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.165', 'subgroup_hash': 165, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186248433
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 738, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.149', 'subgroup_hash': 149, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186248434
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 739, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.165', 'subgroup_hash': 165, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186248436
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 740, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.165', 'subgroup_hash': 165, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186248437
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 741, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.165', 'subgroup_hash': 165, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186248438
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 742, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.165', 'subgroup_hash': 165, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186248439
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 743, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.165', 'subgroup_hash': 165, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186248440
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 744, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.165', 'subgroup_hash': 165, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248441
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 27, 'counter': 745, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.177', 'subgroup_hash': 177, 'subgroup_order': 216, 'subgroup_tex': 'C_6^3', 'supersolvable': True, 'sylow': 0}
-
id: 186248442
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 746, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.173', 'subgroup_hash': 173, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
-
id: 186248443
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 747, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.173', 'subgroup_hash': 173, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
-
id: 186248444
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 748, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.107', 'subgroup_hash': 107, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
-
id: 186248445
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 749, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.107', 'subgroup_hash': 107, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
-
id: 186248447
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 750, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.107', 'subgroup_hash': 107, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
-
id: 186248448
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 751, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.107', 'subgroup_hash': 107, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
-
id: 186248449
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 752, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248450
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 753, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248451
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 754, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.126', 'subgroup_hash': 126, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248452
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 755, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.126', 'subgroup_hash': 126, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248453
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 756, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.170', 'subgroup_hash': 170, 'subgroup_order': 216, 'subgroup_tex': 'C_6\\times S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248454
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 757, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248455
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 758, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.122', 'subgroup_hash': 122, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186248456
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 759, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.121', 'subgroup_hash': 121, 'subgroup_order': 216, 'subgroup_tex': 'C_3^3:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186248458
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 760, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.128', 'subgroup_hash': 128, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186248459
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 761, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.128', 'subgroup_hash': 128, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186248460
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 762, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.122', 'subgroup_hash': 122, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186248461
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 763, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.119', 'subgroup_hash': 119, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248462
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 764, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.119', 'subgroup_hash': 119, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248463
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 765, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.170', 'subgroup_hash': 170, 'subgroup_order': 216, 'subgroup_tex': 'C_6\\times S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186248464
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 766, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.121', 'subgroup_hash': 121, 'subgroup_order': 216, 'subgroup_tex': 'C_3^3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186248465
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 767, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.122', 'subgroup_hash': 122, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186248466
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 768, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.129', 'subgroup_hash': 129, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186248467
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 769, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.129', 'subgroup_hash': 129, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186248469
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 770, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.132', 'subgroup_hash': 132, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186248470
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 771, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.120', 'subgroup_hash': 120, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186248471
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 772, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.131', 'subgroup_hash': 131, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186248472
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 773, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.172', 'subgroup_hash': 172, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186248473
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 774, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.132', 'subgroup_hash': 132, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186248474
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 775, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186248475
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 776, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.128', 'subgroup_hash': 128, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186248476
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 777, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.119', 'subgroup_hash': 119, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186248477
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 778, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.126', 'subgroup_hash': 126, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186248478
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 779, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.129', 'subgroup_hash': 129, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186248480
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 780, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.126', 'subgroup_hash': 126, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248481
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 781, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.ek1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.120', 'subgroup_hash': 120, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248482
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 782, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.el1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.131', 'subgroup_hash': 131, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248483
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 783, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.em1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.123', 'subgroup_hash': 123, 'subgroup_order': 216, 'subgroup_tex': 'C_3^3:Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 186248484
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 784, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.en1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.123', 'subgroup_hash': 123, 'subgroup_order': 216, 'subgroup_tex': 'C_3^3:Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 186248485
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 785, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.eo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.133', 'subgroup_hash': 133, 'subgroup_order': 216, 'subgroup_tex': 'C_3^3:Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 186248486
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 786, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.ep1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.99', 'subgroup_hash': 99, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
-
id: 186248487
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 787, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.eq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.99', 'subgroup_hash': 99, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
-
id: 186248488
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 788, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.er1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.167', 'subgroup_hash': 167, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
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id: 186248489
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 54, 'counter': 789, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.es1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.176', 'subgroup_hash': 176, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186248491
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 790, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.et1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.107', 'subgroup_hash': 107, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
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id: 186248492
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 791, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.eu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.eu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.139', 'subgroup_hash': 139, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': True, 'sylow': 0}
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id: 186248493
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 792, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.ev1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ev1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.174', 'subgroup_hash': 174, 'subgroup_order': 216, 'subgroup_tex': 'S_3\\times C_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248494
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 793, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.ew1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ew1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.166', 'subgroup_hash': 166, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
-
id: 186248495
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 794, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.ex1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ex1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.166', 'subgroup_hash': 166, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
-
id: 186248496
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 795, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.ey1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ey1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.92', 'subgroup_hash': 92, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248497
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 796, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.ez1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ez1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.92', 'subgroup_hash': 92, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248498
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 797, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.fa1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.164', 'subgroup_hash': 164, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248499
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 798, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.fb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.166', 'subgroup_hash': 166, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
-
id: 186248500
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 799, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.fc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.95', 'subgroup_hash': 95, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248503
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 800, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.fd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.95', 'subgroup_hash': 95, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248504
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 801, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.fe1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.95', 'subgroup_hash': 95, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248505
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 802, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.ff1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ff1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.95', 'subgroup_hash': 95, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248506
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 803, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.fg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.144', 'subgroup_hash': 144, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': True, 'sylow': 0}
-
id: 186248507
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 804, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.fh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.164', 'subgroup_hash': 164, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248508
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 805, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.fi1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.164', 'subgroup_hash': 164, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248509
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 806, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.fj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.99', 'subgroup_hash': 99, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
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id: 186248510
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 807, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.fk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.99', 'subgroup_hash': 99, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
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id: 186248511
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 808, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.fl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.175', 'subgroup_hash': 175, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': True, 'sylow': 0}
-
id: 186248512
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 809, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.fm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.139', 'subgroup_hash': 139, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': True, 'sylow': 0}
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id: 186248514
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 810, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.fn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.163', 'subgroup_hash': 163, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2\\times S_4', 'supersolvable': False, 'sylow': 0}
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id: 186248515
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 811, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.fo1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.163', 'subgroup_hash': 163, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248516
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 812, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.fp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.95', 'subgroup_hash': 95, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248517
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 813, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.fq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.176', 'subgroup_hash': 176, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186248518
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 814, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.fr1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.92', 'subgroup_hash': 92, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186248519
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 815, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.fs1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.92', 'subgroup_hash': 92, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186248520
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 816, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.ft1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ft1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.144', 'subgroup_hash': 144, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': True, 'sylow': 0}
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id: 186248521
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 817, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.fu1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.165', 'subgroup_hash': 165, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186248522
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 818, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.fv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.138', 'subgroup_hash': 138, 'subgroup_order': 216, 'subgroup_tex': 'C_6.C_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186248523
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 819, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.fw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.143', 'subgroup_hash': 143, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2.C_6', 'supersolvable': True, 'sylow': 0}
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id: 186248525
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 820, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.fx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
-
id: 186248526
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 821, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.fy1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.102', 'subgroup_hash': 102, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186248527
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 822, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.fz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
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id: 186248528
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 823, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.ga1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ga1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
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id: 186248529
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 824, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.144.gb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
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id: 186248530
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 825, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.162.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.302', 'subgroup_hash': 302, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186248531
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 826, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.162.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.302', 'subgroup_hash': 302, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186248532
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 827, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.162.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1524', 'subgroup_hash': 1524, 'subgroup_order': 192, 'subgroup_tex': 'D_{12}:C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 186248533
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 828, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.162.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.302', 'subgroup_hash': 302, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186248534
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 829, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.162.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1524', 'subgroup_hash': 1524, 'subgroup_order': 192, 'subgroup_tex': 'D_{12}:C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 186248536
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 830, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.162.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.302', 'subgroup_hash': 302, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186248537
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 831, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.162.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.302', 'subgroup_hash': 302, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186248538
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 832, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.162.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.803', 'subgroup_hash': 803, 'subgroup_order': 192, 'subgroup_tex': '(C_2\\times C_{12}):D_4', 'supersolvable': True, 'sylow': 0}
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id: 186248539
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 833, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.162.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.300', 'subgroup_hash': 300, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186248540
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 834, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.162.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.803', 'subgroup_hash': 803, 'subgroup_order': 192, 'subgroup_tex': '(C_2\\times C_{12}):D_4', 'supersolvable': True, 'sylow': 0}
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id: 186248541
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 835, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.162.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.300', 'subgroup_hash': 300, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186248542
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 836, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.162.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.300', 'subgroup_hash': 300, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186248543
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 837, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.162.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.300', 'subgroup_hash': 300, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186248544
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 838, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.162.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.300', 'subgroup_hash': 300, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186248545
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 839, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.162.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1000', 'subgroup_hash': 1000, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:A_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248547
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 840, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.162.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1538', 'subgroup_hash': 1538, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186248548
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 841, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.162.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1488', 'subgroup_hash': 1488, 'subgroup_order': 192, 'subgroup_tex': 'C_2\\times \\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
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id: 186248549
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 842, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.162.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1538', 'subgroup_hash': 1538, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186248550
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 843, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.162.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1147', 'subgroup_hash': 1147, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186248551
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 844, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.162.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1147', 'subgroup_hash': 1147, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186248552
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 845, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.162.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1147', 'subgroup_hash': 1147, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186248553
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 846, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.162.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1147', 'subgroup_hash': 1147, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186248554
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 847, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.162.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1147', 'subgroup_hash': 1147, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186248555
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 848, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.162.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1147', 'subgroup_hash': 1147, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186248556
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 48, 'counter': 849, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.162.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.890', 'subgroup_hash': 890, 'subgroup_order': 192, 'subgroup_tex': 'C_3\\times C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 186248558
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 16, 'counter': 850, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.162.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.591', 'subgroup_hash': 591, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186248559
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 16, 'counter': 851, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.162.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.955', 'subgroup_hash': 955, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186248560
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 16, 'counter': 852, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.162.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.955', 'subgroup_hash': 955, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186248561
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 16, 'counter': 853, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.162.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.890', 'subgroup_hash': 890, 'subgroup_order': 192, 'subgroup_tex': 'C_3\\times C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 186248562
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 16, 'counter': 854, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.162.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.955', 'subgroup_hash': 955, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186248563
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 48, 'counter': 855, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.162.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.591', 'subgroup_hash': 591, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186248564
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 48, 'counter': 856, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.162.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.591', 'subgroup_hash': 591, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186248565
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 857, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.162.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.955', 'subgroup_hash': 955, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186248566
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 858, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.162.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.591', 'subgroup_hash': 591, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186248567
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 859, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.162.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.955', 'subgroup_hash': 955, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186248569
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 860, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.162.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.955', 'subgroup_hash': 955, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186248570
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 861, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.162.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.591', 'subgroup_hash': 591, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186248571
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 862, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.192.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.48', 'subgroup_hash': 48, 'subgroup_order': 162, 'subgroup_tex': 'C_6\\times \\He_3', 'supersolvable': True, 'sylow': 0}
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id: 186248572
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 863, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.192.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
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id: 186248573
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 864, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.192.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.40', 'subgroup_hash': 40, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
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id: 186248574
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 865, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.192.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.40', 'subgroup_hash': 40, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
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id: 186248575
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 866, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.192.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.35', 'subgroup_hash': 35, 'subgroup_order': 162, 'subgroup_tex': 'S_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
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id: 186248576
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 867, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.192.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.34', 'subgroup_hash': 34, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
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id: 186248577
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 868, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.192.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
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id: 186248578
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 869, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.192.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.34', 'subgroup_hash': 34, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
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id: 186248580
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 870, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.192.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.34', 'subgroup_hash': 34, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
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id: 186248581
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 871, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.192.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
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id: 186248582
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 872, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.192.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.34', 'subgroup_hash': 34, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
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id: 186248583
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 873, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.192.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.46', 'subgroup_hash': 46, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186248584
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 27, 'counter': 874, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.192.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186248585
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 875, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.192.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186248586
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 876, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.192.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186248587
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 877, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.192.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 186248588
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 878, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.192.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186248589
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 879, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.192.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.40', 'subgroup_hash': 40, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
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id: 186248591
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 880, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.192.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.40', 'subgroup_hash': 40, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
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id: 186248592
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 881, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.192.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.40', 'subgroup_hash': 40, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
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id: 186248593
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 882, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.192.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186248594
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 144, 'counter': 883, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '31104.fx.216.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '216.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '216.102', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 102, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6.S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '144.194', 'subgroup_hash': 194, 'subgroup_order': 144, 'subgroup_tex': 'C_2^4:C_3^2', 'supersolvable': False, 'sylow': 0}
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id: 186248595
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': True, 'core_order': 144, 'counter': 884, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '31104.fx.216.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '216.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '216.162', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 162, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3^3', 'simple': False, 'solvable': True, 'special_labels': ['S', 'D2', 'C6', 'S', 'D2', 'C6'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '144.197', 'subgroup_hash': 197, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2\\times C_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186248596
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 885, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.172', 'subgroup_hash': 172, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186248597
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 886, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186248598
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 887, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186248599
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 888, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186248600
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 889, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.172', 'subgroup_hash': 172, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186248602
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 890, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186248603
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 891, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186248604
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 892, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186248605
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 893, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.172', 'subgroup_hash': 172, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186248606
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 894, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186248607
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 895, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186248608
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 896, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186248609
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 897, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.196', 'subgroup_hash': 196, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 186248610
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 898, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186248611
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 899, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186248614
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 900, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.149', 'subgroup_hash': 149, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2.S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186248615
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 901, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.149', 'subgroup_hash': 149, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2.S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186248616
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 902, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.169', 'subgroup_hash': 169, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186248617
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 903, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.169', 'subgroup_hash': 169, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186248618
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 904, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.149', 'subgroup_hash': 149, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2.S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186248619
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 905, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.149', 'subgroup_hash': 149, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2.S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186248620
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 906, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.149', 'subgroup_hash': 149, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2.S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186248621
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 907, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.162', 'subgroup_hash': 162, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186248622
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 908, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.163', 'subgroup_hash': 163, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
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id: 186248623
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 909, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.172', 'subgroup_hash': 172, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186248625
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 910, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.167', 'subgroup_hash': 167, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 186248626
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 911, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186248627
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 912, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186248628
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 913, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186248629
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 914, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.161', 'subgroup_hash': 161, 'subgroup_order': 144, 'subgroup_tex': 'D_{12}:C_6', 'supersolvable': True, 'sylow': 0}
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id: 186248630
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 915, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.153', 'subgroup_hash': 153, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186248631
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 916, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.147', 'subgroup_hash': 147, 'subgroup_order': 144, 'subgroup_tex': 'D_6.D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186248632
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 917, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.162', 'subgroup_hash': 162, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186248633
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 918, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.163', 'subgroup_hash': 163, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
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id: 186248634
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 919, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186248636
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 920, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.148', 'subgroup_hash': 148, 'subgroup_order': 144, 'subgroup_tex': 'D_6.D_6', 'supersolvable': True, 'sylow': 0}
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id: 186248637
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 921, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186248638
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 922, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.148', 'subgroup_hash': 148, 'subgroup_order': 144, 'subgroup_tex': 'D_6.D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186248639
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 923, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.153', 'subgroup_hash': 153, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186248640
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 924, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.147', 'subgroup_hash': 147, 'subgroup_order': 144, 'subgroup_tex': 'D_6.D_6', 'supersolvable': True, 'sylow': 0}
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id: 186248641
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 925, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.177', 'subgroup_hash': 177, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248642
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 926, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.177', 'subgroup_hash': 177, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248643
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 927, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.151', 'subgroup_hash': 151, 'subgroup_order': 144, 'subgroup_tex': 'C_6:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186248644
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 928, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.151', 'subgroup_hash': 151, 'subgroup_order': 144, 'subgroup_tex': 'C_6:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186248645
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 929, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.bt2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bt2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.151', 'subgroup_hash': 151, 'subgroup_order': 144, 'subgroup_tex': 'C_6:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186248647
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 930, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.151', 'subgroup_hash': 151, 'subgroup_order': 144, 'subgroup_tex': 'C_6:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186248648
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 931, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.151', 'subgroup_hash': 151, 'subgroup_order': 144, 'subgroup_tex': 'C_6:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186248649
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 932, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.151', 'subgroup_hash': 151, 'subgroup_order': 144, 'subgroup_tex': 'C_6:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186248650
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 933, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.151', 'subgroup_hash': 151, 'subgroup_order': 144, 'subgroup_tex': 'C_6:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186248651
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 934, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.151', 'subgroup_hash': 151, 'subgroup_order': 144, 'subgroup_tex': 'C_6:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186248652
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 935, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.170', 'subgroup_hash': 170, 'subgroup_order': 144, 'subgroup_tex': 'C_6:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186248653
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 936, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.65', 'subgroup_hash': 65, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186248654
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 937, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.65', 'subgroup_hash': 65, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186248655
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 938, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.95', 'subgroup_hash': 95, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186248656
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 939, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.95', 'subgroup_hash': 95, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186248658
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 940, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.65', 'subgroup_hash': 65, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186248659
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 941, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ce2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ce2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.65', 'subgroup_hash': 65, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186248660
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 942, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.65', 'subgroup_hash': 65, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186248661
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 943, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.65', 'subgroup_hash': 65, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186248662
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 944, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.151', 'subgroup_hash': 151, 'subgroup_order': 144, 'subgroup_tex': 'C_6:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186248663
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 945, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.151', 'subgroup_hash': 151, 'subgroup_order': 144, 'subgroup_tex': 'C_6:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186248664
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 946, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.170', 'subgroup_hash': 170, 'subgroup_order': 144, 'subgroup_tex': 'C_6:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186248665
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 947, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.65', 'subgroup_hash': 65, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186248666
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 948, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.95', 'subgroup_hash': 95, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186248667
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 949, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.65', 'subgroup_hash': 65, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186248669
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 950, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.65', 'subgroup_hash': 65, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186248670
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 951, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.196', 'subgroup_hash': 196, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248671
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 952, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.196', 'subgroup_hash': 196, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248672
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 953, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.196', 'subgroup_hash': 196, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248673
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 954, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.196', 'subgroup_hash': 196, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248674
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 955, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.196', 'subgroup_hash': 196, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248675
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 956, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.179', 'subgroup_hash': 179, 'subgroup_order': 144, 'subgroup_tex': 'C_4:C_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248676
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 957, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.167', 'subgroup_hash': 167, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248677
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 958, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.167', 'subgroup_hash': 167, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248678
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 959, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.167', 'subgroup_hash': 167, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248680
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 960, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.167', 'subgroup_hash': 167, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248681
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 961, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.167', 'subgroup_hash': 167, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248682
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 962, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.167', 'subgroup_hash': 167, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248683
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 963, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.177', 'subgroup_hash': 177, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248684
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 964, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.179', 'subgroup_hash': 179, 'subgroup_order': 144, 'subgroup_tex': 'C_4:C_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248685
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 965, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.167', 'subgroup_hash': 167, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248686
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 966, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.167', 'subgroup_hash': 167, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248687
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 967, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.196', 'subgroup_hash': 196, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248688
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 968, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.196', 'subgroup_hash': 196, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248689
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 969, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.196', 'subgroup_hash': 196, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248691
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 970, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.196', 'subgroup_hash': 196, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248692
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 971, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.196', 'subgroup_hash': 196, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248693
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 972, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.167', 'subgroup_hash': 167, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248694
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 973, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.167', 'subgroup_hash': 167, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248695
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 974, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.177', 'subgroup_hash': 177, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186248696
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 975, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.102', 'subgroup_hash': 102, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 186248697
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 976, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.84', 'subgroup_hash': 84, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 186248698
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 977, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.84', 'subgroup_hash': 84, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186248699
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 978, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.84', 'subgroup_hash': 84, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186248700
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 979, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.84', 'subgroup_hash': 84, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 186248702
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 980, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.84', 'subgroup_hash': 84, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186248703
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 981, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.100', 'subgroup_hash': 100, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186248704
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 982, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.84', 'subgroup_hash': 84, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 186248705
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 983, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.84', 'subgroup_hash': 84, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 186248706
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 984, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.102', 'subgroup_hash': 102, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186248707
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 985, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.84', 'subgroup_hash': 84, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 186248708
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 986, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.100', 'subgroup_hash': 100, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 186248709
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 987, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.84', 'subgroup_hash': 84, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186248710
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 988, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.84', 'subgroup_hash': 84, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 186248711
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 989, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.189', 'subgroup_hash': 189, 'subgroup_order': 144, 'subgroup_tex': 'C_6:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248713
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 990, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.153', 'subgroup_hash': 153, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186248714
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 991, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186248715
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 992, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
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id: 186248716
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 993, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
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id: 186248717
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 994, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.153', 'subgroup_hash': 153, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186248718
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 995, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.153', 'subgroup_hash': 153, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186248719
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 996, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
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id: 186248720
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 997, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
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id: 186248721
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 998, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
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id: 186248722
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 999, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ek1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
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id: 186245338
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1000, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.el1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.172', 'subgroup_hash': 172, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245339
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1001, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.em1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245340
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1002, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.en1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245341
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1003, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.eo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245342
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1004, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ep1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.172', 'subgroup_hash': 172, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245343
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1005, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.eq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
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id: 186245344
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1006, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.er1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
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id: 186245345
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1007, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.es1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
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id: 186245346
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1008, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.et1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245347
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1009, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.eu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.eu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245349
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1010, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ev1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ev1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245350
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1011, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ew1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ew1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.190', 'subgroup_hash': 190, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
-
id: 186245351
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1012, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ex1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ex1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.190', 'subgroup_hash': 190, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
-
id: 186245352
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1013, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ey1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ey1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.190', 'subgroup_hash': 190, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
-
id: 186245353
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1014, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ez1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ez1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.196', 'subgroup_hash': 196, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245354
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 1015, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.fa1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.fa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.196', 'subgroup_hash': 196, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245355
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1016, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.fb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.fb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.196', 'subgroup_hash': 196, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245356
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1017, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.fc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.fc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.196', 'subgroup_hash': 196, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245357
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1018, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.fd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.fd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.196', 'subgroup_hash': 196, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245358
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 1019, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.fe1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.fe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.179', 'subgroup_hash': 179, 'subgroup_order': 144, 'subgroup_tex': 'C_4:C_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245360
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 1020, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ff1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ff1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.167', 'subgroup_hash': 167, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245361
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 1021, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.fg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.fg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.188', 'subgroup_hash': 188, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186245362
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 1022, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.fh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.fh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.188', 'subgroup_hash': 188, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186245363
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 1023, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.fi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.fi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.167', 'subgroup_hash': 167, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245364
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 1024, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.fj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.fj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.167', 'subgroup_hash': 167, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245365
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1025, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.fk1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.fk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.188', 'subgroup_hash': 188, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186245366
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1026, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.fl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.fl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.188', 'subgroup_hash': 188, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186245367
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1027, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.fm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.fm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.188', 'subgroup_hash': 188, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186245368
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1028, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.fn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.fn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.188', 'subgroup_hash': 188, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186245369
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1029, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.fo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.fo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.190', 'subgroup_hash': 190, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
-
id: 186245371
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1030, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.fp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.fp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.190', 'subgroup_hash': 190, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
-
id: 186245372
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1031, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.fq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.fq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.190', 'subgroup_hash': 190, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
-
id: 186245373
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1032, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.fr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.fr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.196', 'subgroup_hash': 196, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245374
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 1033, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.fs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.fs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.196', 'subgroup_hash': 196, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245375
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1034, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ft1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ft1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.196', 'subgroup_hash': 196, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245376
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1035, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.fu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.fu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.196', 'subgroup_hash': 196, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245377
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1036, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.fv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.fv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.196', 'subgroup_hash': 196, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245378
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1037, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.fw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.fw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.167', 'subgroup_hash': 167, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245379
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1038, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.fx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.fx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.167', 'subgroup_hash': 167, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245380
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1039, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.fy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.fy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.167', 'subgroup_hash': 167, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245382
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1040, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.fz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.fz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.189', 'subgroup_hash': 189, 'subgroup_order': 144, 'subgroup_tex': 'C_6:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186245383
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1041, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ga1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ga1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.177', 'subgroup_hash': 177, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245384
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1042, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.gb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.gb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.189', 'subgroup_hash': 189, 'subgroup_order': 144, 'subgroup_tex': 'C_6:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186245385
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1043, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.gc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.gc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.189', 'subgroup_hash': 189, 'subgroup_order': 144, 'subgroup_tex': 'C_6:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186245386
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1044, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.gd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.gd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.189', 'subgroup_hash': 189, 'subgroup_order': 144, 'subgroup_tex': 'C_6:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186245387
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 1045, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ge1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ge1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.84', 'subgroup_hash': 84, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 186245388
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1046, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.gf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.gf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.84', 'subgroup_hash': 84, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 186245389
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 1047, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.gg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.gg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.123', 'subgroup_hash': 123, 'subgroup_order': 144, 'subgroup_tex': 'A_4:C_{12}', 'supersolvable': False, 'sylow': 0}
-
id: 186245390
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1048, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.gh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.gh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.126', 'subgroup_hash': 126, 'subgroup_order': 144, 'subgroup_tex': 'C_6.S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186245391
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 1049, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.gi1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.gi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.123', 'subgroup_hash': 123, 'subgroup_order': 144, 'subgroup_tex': 'A_4:C_{12}', 'supersolvable': False, 'sylow': 0}
-
id: 186245393
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 1050, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.gj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.gj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.102', 'subgroup_hash': 102, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 186245394
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1051, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.gk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.gk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.100', 'subgroup_hash': 100, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 186245395
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 1052, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.gl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.gl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.84', 'subgroup_hash': 84, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 186245396
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 1053, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.gm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.gm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.84', 'subgroup_hash': 84, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 186245397
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1054, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.gn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.gn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.84', 'subgroup_hash': 84, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 186245398
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1055, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.go1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.go1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.84', 'subgroup_hash': 84, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 186245399
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1056, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.gp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.gp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.123', 'subgroup_hash': 123, 'subgroup_order': 144, 'subgroup_tex': 'A_4:C_{12}', 'supersolvable': False, 'sylow': 0}
-
id: 186245400
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1057, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.gq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.gq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.126', 'subgroup_hash': 126, 'subgroup_order': 144, 'subgroup_tex': 'C_6.S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186245401
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1058, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.gr1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.gr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.123', 'subgroup_hash': 123, 'subgroup_order': 144, 'subgroup_tex': 'A_4:C_{12}', 'supersolvable': False, 'sylow': 0}
-
id: 186245402
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1059, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.gs1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.gs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.126', 'subgroup_hash': 126, 'subgroup_order': 144, 'subgroup_tex': 'C_6.S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186245404
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1060, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.gt1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.gt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.126', 'subgroup_hash': 126, 'subgroup_order': 144, 'subgroup_tex': 'C_6.S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186245405
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1061, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.gu1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.gu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.123', 'subgroup_hash': 123, 'subgroup_order': 144, 'subgroup_tex': 'A_4:C_{12}', 'supersolvable': False, 'sylow': 0}
-
id: 186245406
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1062, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.gv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.gv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.123', 'subgroup_hash': 123, 'subgroup_order': 144, 'subgroup_tex': 'A_4:C_{12}', 'supersolvable': False, 'sylow': 0}
-
id: 186245407
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 48, 'counter': 1063, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.gw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.gw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.197', 'subgroup_hash': 197, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2\\times C_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245408
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 48, 'counter': 1064, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.gx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.gx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.193', 'subgroup_hash': 193, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2:C_6^2', 'supersolvable': False, 'sylow': 0}
-
id: 186245409
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 48, 'counter': 1065, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.gy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.gy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.194', 'subgroup_hash': 194, 'subgroup_order': 144, 'subgroup_tex': 'C_2^4:C_3^2', 'supersolvable': False, 'sylow': 0}
-
id: 186245410
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 48, 'counter': 1066, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.gz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.gz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.194', 'subgroup_hash': 194, 'subgroup_order': 144, 'subgroup_tex': 'C_2^4:C_3^2', 'supersolvable': False, 'sylow': 0}
-
id: 186245411
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 48, 'counter': 1067, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ha1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ha1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.193', 'subgroup_hash': 193, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2:C_6^2', 'supersolvable': False, 'sylow': 0}
-
id: 186245412
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 48, 'counter': 1068, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.hb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.hb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.194', 'subgroup_hash': 194, 'subgroup_order': 144, 'subgroup_tex': 'C_2^4:C_3^2', 'supersolvable': False, 'sylow': 0}
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id: 186245413
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 48, 'counter': 1069, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.hb2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.hb2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.194', 'subgroup_hash': 194, 'subgroup_order': 144, 'subgroup_tex': 'C_2^4:C_3^2', 'supersolvable': False, 'sylow': 0}
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id: 186245415
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 16, 'counter': 1070, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.hc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.hc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.197', 'subgroup_hash': 197, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2\\times C_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186245416
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 16, 'counter': 1071, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.hd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.hd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.193', 'subgroup_hash': 193, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2:C_6^2', 'supersolvable': False, 'sylow': 0}
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id: 186245417
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 16, 'counter': 1072, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.he1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.he1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.193', 'subgroup_hash': 193, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2:C_6^2', 'supersolvable': False, 'sylow': 0}
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id: 186245418
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 16, 'counter': 1073, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.hf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.hf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.194', 'subgroup_hash': 194, 'subgroup_order': 144, 'subgroup_tex': 'C_2^4:C_3^2', 'supersolvable': False, 'sylow': 0}
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id: 186245419
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 16, 'counter': 1074, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.hg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.hg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.193', 'subgroup_hash': 193, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2:C_6^2', 'supersolvable': False, 'sylow': 0}
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id: 186245420
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 16, 'counter': 1075, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.hh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.hh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.193', 'subgroup_hash': 193, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2:C_6^2', 'supersolvable': False, 'sylow': 0}
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id: 186245421
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 16, 'counter': 1076, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.hh2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.hh2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.193', 'subgroup_hash': 193, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2:C_6^2', 'supersolvable': False, 'sylow': 0}
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id: 186245422
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 16, 'counter': 1077, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.hi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.hi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.194', 'subgroup_hash': 194, 'subgroup_order': 144, 'subgroup_tex': 'C_2^4:C_3^2', 'supersolvable': False, 'sylow': 0}
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id: 186245423
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 16, 'counter': 1078, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.hj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.hj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.184', 'subgroup_hash': 184, 'subgroup_order': 144, 'subgroup_tex': 'A_4^2', 'supersolvable': False, 'sylow': 0}
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id: 186245424
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 16, 'counter': 1079, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.hk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.hk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.184', 'subgroup_hash': 184, 'subgroup_order': 144, 'subgroup_tex': 'A_4^2', 'supersolvable': False, 'sylow': 0}
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id: 186245426
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 16, 'counter': 1080, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.hl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.hl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.184', 'subgroup_hash': 184, 'subgroup_order': 144, 'subgroup_tex': 'A_4^2', 'supersolvable': False, 'sylow': 0}
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id: 186245427
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 16, 'counter': 1081, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.hm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.hm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.184', 'subgroup_hash': 184, 'subgroup_order': 144, 'subgroup_tex': 'A_4^2', 'supersolvable': False, 'sylow': 0}
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id: 186245428
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 16, 'counter': 1082, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.hn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.hn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.184', 'subgroup_hash': 184, 'subgroup_order': 144, 'subgroup_tex': 'A_4^2', 'supersolvable': False, 'sylow': 0}
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id: 186245429
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 16, 'counter': 1083, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ho1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ho1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.184', 'subgroup_hash': 184, 'subgroup_order': 144, 'subgroup_tex': 'A_4^2', 'supersolvable': False, 'sylow': 0}
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id: 186245430
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 16, 'counter': 1084, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.hp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.hp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.184', 'subgroup_hash': 184, 'subgroup_order': 144, 'subgroup_tex': 'A_4^2', 'supersolvable': False, 'sylow': 0}
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id: 186245431
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 16, 'counter': 1085, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.hp2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.hp2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.184', 'subgroup_hash': 184, 'subgroup_order': 144, 'subgroup_tex': 'A_4^2', 'supersolvable': False, 'sylow': 0}
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id: 186245432
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1086, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.hq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.hq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245433
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1087, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.hr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.hr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.149', 'subgroup_hash': 149, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2.S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245434
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1088, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.hs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.hs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245435
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1089, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ht1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ht1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.145', 'subgroup_hash': 145, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245437
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1090, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.hu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.hu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.143', 'subgroup_hash': 143, 'subgroup_order': 144, 'subgroup_tex': 'C_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186245438
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1091, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.hv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.hv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.143', 'subgroup_hash': 143, 'subgroup_order': 144, 'subgroup_tex': 'C_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186245439
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1092, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.hw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.hw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186245440
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1093, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.hx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.hx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245441
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1094, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.hy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.hy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186245442
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1095, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.hz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.hz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.145', 'subgroup_hash': 145, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245443
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1096, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ia1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ia1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.149', 'subgroup_hash': 149, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2.S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186245444
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1097, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ib1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ib1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.143', 'subgroup_hash': 143, 'subgroup_order': 144, 'subgroup_tex': 'C_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186245445
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1098, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ic1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ic1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.140', 'subgroup_hash': 140, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245446
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1099, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.id1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.id1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.140', 'subgroup_hash': 140, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245449
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ie1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ie1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.153', 'subgroup_hash': 153, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245450
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.if1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.if1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.147', 'subgroup_hash': 147, 'subgroup_order': 144, 'subgroup_tex': 'D_6.D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245451
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ig1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ig1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.151', 'subgroup_hash': 151, 'subgroup_order': 144, 'subgroup_tex': 'C_6:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245452
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ih1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ih1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245453
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ii1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ii1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.147', 'subgroup_hash': 147, 'subgroup_order': 144, 'subgroup_tex': 'D_6.D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245454
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ij1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ij1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.147', 'subgroup_hash': 147, 'subgroup_order': 144, 'subgroup_tex': 'D_6.D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245455
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ik1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ik1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.151', 'subgroup_hash': 151, 'subgroup_order': 144, 'subgroup_tex': 'C_6:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186245456
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.il1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.il1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.139', 'subgroup_hash': 139, 'subgroup_order': 144, 'subgroup_tex': 'D_{12}:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186245457
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.im1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.im1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.153', 'subgroup_hash': 153, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245458
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.in1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.in1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.144', 'subgroup_hash': 144, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186245460
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.io1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.io1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.144', 'subgroup_hash': 144, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186245461
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ip1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ip1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.142', 'subgroup_hash': 142, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245462
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.iq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.iq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.144', 'subgroup_hash': 144, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186245463
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ir1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ir1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.144', 'subgroup_hash': 144, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186245464
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.is1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.is1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.147', 'subgroup_hash': 147, 'subgroup_order': 144, 'subgroup_tex': 'D_6.D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245465
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.it1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.it1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.141', 'subgroup_hash': 141, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245466
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.iu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.iu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.139', 'subgroup_hash': 139, 'subgroup_order': 144, 'subgroup_tex': 'D_{12}:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186245467
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.iv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.iv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.142', 'subgroup_hash': 142, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245468
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.iw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.iw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.153', 'subgroup_hash': 153, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245469
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ix1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ix1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.153', 'subgroup_hash': 153, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245471
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.iy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.iy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245472
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.iz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.iz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.151', 'subgroup_hash': 151, 'subgroup_order': 144, 'subgroup_tex': 'C_6:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186245473
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ja1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ja1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.153', 'subgroup_hash': 153, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245474
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.jb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.jb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.147', 'subgroup_hash': 147, 'subgroup_order': 144, 'subgroup_tex': 'D_6.D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245475
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.jc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.jc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.153', 'subgroup_hash': 153, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245476
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.jd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.jd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.144', 'subgroup_hash': 144, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186245477
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.je1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.je1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245478
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.jf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.jf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.141', 'subgroup_hash': 141, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245479
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.jg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.jg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.147', 'subgroup_hash': 147, 'subgroup_order': 144, 'subgroup_tex': 'D_6.D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245480
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.jh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.jh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.139', 'subgroup_hash': 139, 'subgroup_order': 144, 'subgroup_tex': 'D_{12}:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186245482
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ji1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ji1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.141', 'subgroup_hash': 141, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245483
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.jj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.jj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.142', 'subgroup_hash': 142, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245484
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.jk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.jk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245485
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.jl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.jl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.141', 'subgroup_hash': 141, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245486
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.jm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.jm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.142', 'subgroup_hash': 142, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245487
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.jn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.jn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.142', 'subgroup_hash': 142, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245488
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.jo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.jo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.144', 'subgroup_hash': 144, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186245489
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.jp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.jp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.142', 'subgroup_hash': 142, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245490
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.jq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.jq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.190', 'subgroup_hash': 190, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
-
id: 186245491
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.jr1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.jr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186245493
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.js1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.js1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.190', 'subgroup_hash': 190, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
-
id: 186245494
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.jt1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.jt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186245495
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ju1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ju1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186245496
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.jv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.jv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186245497
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.jw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.jw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186245498
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.jx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.jx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.172', 'subgroup_hash': 172, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245499
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.jy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.jy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.196', 'subgroup_hash': 196, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245500
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.jz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.jz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245501
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ka1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ka1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245502
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.kb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.kb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245504
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.kc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.kc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245505
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.kd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.kd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245506
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ke1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ke1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.172', 'subgroup_hash': 172, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245507
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.kf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.kf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245508
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.kg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.kg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245509
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.kh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.kh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245510
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ki1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ki1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.169', 'subgroup_hash': 169, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245511
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.kj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.kj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.149', 'subgroup_hash': 149, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2.S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245512
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.kk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.kk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.149', 'subgroup_hash': 149, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2.S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186245513
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.kl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.kl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.149', 'subgroup_hash': 149, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2.S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245515
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.km1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.km1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.162', 'subgroup_hash': 162, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245516
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.kn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.kn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.172', 'subgroup_hash': 172, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245517
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ko1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ko1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.163', 'subgroup_hash': 163, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245518
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.kp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.kp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.163', 'subgroup_hash': 163, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245519
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.kq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.kq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.167', 'subgroup_hash': 167, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 186245520
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.kr1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.kr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.188', 'subgroup_hash': 188, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
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id: 186245521
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ks1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ks1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.188', 'subgroup_hash': 188, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
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id: 186245522
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.kt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.kt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.177', 'subgroup_hash': 177, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 186245523
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ku1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ku1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.188', 'subgroup_hash': 188, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
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id: 186245524
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.kv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.kv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245526
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.kw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.kw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245527
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.kx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.kx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245528
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 1172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ky1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ky1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.162', 'subgroup_hash': 162, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245529
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.kz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.kz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245530
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 1174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.la1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.la1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.163', 'subgroup_hash': 163, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245531
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.lb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.lb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.148', 'subgroup_hash': 148, 'subgroup_order': 144, 'subgroup_tex': 'D_6.D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245532
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.lc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.lc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.161', 'subgroup_hash': 161, 'subgroup_order': 144, 'subgroup_tex': 'D_{12}:C_6', 'supersolvable': True, 'sylow': 0}
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id: 186245533
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 1177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ld1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ld1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.147', 'subgroup_hash': 147, 'subgroup_order': 144, 'subgroup_tex': 'D_6.D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245534
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.le1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.le1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.167', 'subgroup_hash': 167, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 186245535
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 1179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.lf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.lf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.162', 'subgroup_hash': 162, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245537
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.lg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.lg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.153', 'subgroup_hash': 153, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245538
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.lh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.lh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186245539
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 1182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.li1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.li1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186245540
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.lj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.lj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.151', 'subgroup_hash': 151, 'subgroup_order': 144, 'subgroup_tex': 'C_6:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186245541
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.lj2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.lj2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.151', 'subgroup_hash': 151, 'subgroup_order': 144, 'subgroup_tex': 'C_6:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186245542
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.lk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.lk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.151', 'subgroup_hash': 151, 'subgroup_order': 144, 'subgroup_tex': 'C_6:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186245543
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ll1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ll1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.162', 'subgroup_hash': 162, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245544
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.lm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.lm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
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id: 186245545
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ln1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ln1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186245546
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 1189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.lo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.lo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.153', 'subgroup_hash': 153, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245548
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.lp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.lp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.189', 'subgroup_hash': 189, 'subgroup_order': 144, 'subgroup_tex': 'C_6:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186245549
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 1191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.lq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.lq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.163', 'subgroup_hash': 163, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245550
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.lr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.lr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.161', 'subgroup_hash': 161, 'subgroup_order': 144, 'subgroup_tex': 'D_{12}:C_6', 'supersolvable': True, 'sylow': 0}
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id: 186245551
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ls1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ls1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.148', 'subgroup_hash': 148, 'subgroup_order': 144, 'subgroup_tex': 'D_6.D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245552
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.lt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.lt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.147', 'subgroup_hash': 147, 'subgroup_order': 144, 'subgroup_tex': 'D_6.D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245553
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.lu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.lu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.151', 'subgroup_hash': 151, 'subgroup_order': 144, 'subgroup_tex': 'C_6:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186245554
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.lv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.lv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.151', 'subgroup_hash': 151, 'subgroup_order': 144, 'subgroup_tex': 'C_6:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245555
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.lw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.lw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.151', 'subgroup_hash': 151, 'subgroup_order': 144, 'subgroup_tex': 'C_6:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245556
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.lx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.lx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.147', 'subgroup_hash': 147, 'subgroup_order': 144, 'subgroup_tex': 'D_6.D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245557
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ly1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ly1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.147', 'subgroup_hash': 147, 'subgroup_order': 144, 'subgroup_tex': 'D_6.D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245560
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.lz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.lz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186245561
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 1201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ma1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ma1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186245562
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.mb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.mb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.153', 'subgroup_hash': 153, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245563
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.mc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.mc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.189', 'subgroup_hash': 189, 'subgroup_order': 144, 'subgroup_tex': 'C_6:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186245564
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.md1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.md1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.153', 'subgroup_hash': 153, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245565
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.me1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.me1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.170', 'subgroup_hash': 170, 'subgroup_order': 144, 'subgroup_tex': 'C_6:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245566
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.mf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.mf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245567
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.mg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.mg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.172', 'subgroup_hash': 172, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245568
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.mh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.mh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245569
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.mi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.mi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245571
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.mj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.mj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245572
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.mk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.mk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.95', 'subgroup_hash': 95, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245573
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.ml1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ml1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.65', 'subgroup_hash': 65, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245574
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.mm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.mm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.65', 'subgroup_hash': 65, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245575
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.mm2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.mm2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.65', 'subgroup_hash': 65, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186245576
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.216.mn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.mn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.65', 'subgroup_hash': 65, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245577
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 1216, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '31104.fx.243.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '243.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 243, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1755', 'subgroup_hash': 1755, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 2}
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id: 186245578
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 27, 'counter': 1217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.45', 'subgroup_hash': 45, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times C_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186245579
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245580
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.25', 'subgroup_hash': 25, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245582
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.25', 'subgroup_hash': 25, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245583
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 54, 'counter': 1221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.44', 'subgroup_hash': 44, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245584
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 1222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245585
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 1223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245586
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 1224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245587
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.28', 'subgroup_hash': 28, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245588
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245589
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.25', 'subgroup_hash': 25, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245590
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.25', 'subgroup_hash': 25, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245591
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 1229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.44', 'subgroup_hash': 44, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245593
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 1230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.44', 'subgroup_hash': 44, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245594
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 1231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.44', 'subgroup_hash': 44, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245595
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 1232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245596
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.25', 'subgroup_hash': 25, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245597
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.25', 'subgroup_hash': 25, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245598
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.44', 'subgroup_hash': 44, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245599
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 1236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.32', 'subgroup_hash': 32, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245600
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 1237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.33', 'subgroup_hash': 33, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245601
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 1238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.32', 'subgroup_hash': 32, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186245602
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.34', 'subgroup_hash': 34, 'subgroup_order': 108, 'subgroup_tex': 'C_3^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 186245604
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 1240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.32', 'subgroup_hash': 32, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186245605
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.11', 'subgroup_hash': 11, 'subgroup_order': 108, 'subgroup_tex': '\\He_3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 186245606
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.8', 'subgroup_hash': 8, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186245607
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.8', 'subgroup_hash': 8, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186245608
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 27, 'counter': 1244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.45', 'subgroup_hash': 45, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times C_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186245609
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 1245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.22', 'subgroup_hash': 22, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:A_4', 'supersolvable': False, 'sylow': 0}
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id: 186245610
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 1246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.22', 'subgroup_hash': 22, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:A_4', 'supersolvable': False, 'sylow': 0}
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id: 186245611
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 1247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.41', 'subgroup_hash': 41, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186245612
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 1248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.41', 'subgroup_hash': 41, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186245613
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 1249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.22', 'subgroup_hash': 22, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:A_4', 'supersolvable': False, 'sylow': 0}
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id: 186245615
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 1250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.22', 'subgroup_hash': 22, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:A_4', 'supersolvable': False, 'sylow': 0}
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id: 186245616
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 27, 'counter': 1251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.45', 'subgroup_hash': 45, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times C_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186245617
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 1252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.45', 'subgroup_hash': 45, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times C_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186245618
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 1253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.41', 'subgroup_hash': 41, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186245619
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 1254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.41', 'subgroup_hash': 41, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186245620
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 1255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.45', 'subgroup_hash': 45, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times C_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186245621
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 1256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.41', 'subgroup_hash': 41, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186245622
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 1257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.41', 'subgroup_hash': 41, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 186245623
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 1258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.30', 'subgroup_hash': 30, 'subgroup_order': 108, 'subgroup_tex': 'C_2^2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
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id: 186245624
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 1259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.22', 'subgroup_hash': 22, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:A_4', 'supersolvable': False, 'sylow': 0}
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id: 186245626
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 1260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.30', 'subgroup_hash': 30, 'subgroup_order': 108, 'subgroup_tex': 'C_2^2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
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id: 186245627
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 1261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.22', 'subgroup_hash': 22, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:A_4', 'supersolvable': False, 'sylow': 0}
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id: 186245628
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 1262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.41', 'subgroup_hash': 41, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186245629
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 1263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.22', 'subgroup_hash': 22, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:A_4', 'supersolvable': False, 'sylow': 0}
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id: 186245630
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 1264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.41', 'subgroup_hash': 41, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186245631
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 1265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.41', 'subgroup_hash': 41, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186245632
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 1266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.22', 'subgroup_hash': 22, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:A_4', 'supersolvable': False, 'sylow': 0}
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id: 186245633
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 1267, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.41', 'subgroup_hash': 41, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186245634
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 1268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.22', 'subgroup_hash': 22, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:A_4', 'supersolvable': False, 'sylow': 0}
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id: 186245635
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 1269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.22', 'subgroup_hash': 22, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:A_4', 'supersolvable': False, 'sylow': 0}
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id: 186245637
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 54, 'counter': 1270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.44', 'subgroup_hash': 44, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245638
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 1271, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245639
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 1272, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245640
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 1273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245641
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 1274, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.44', 'subgroup_hash': 44, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245642
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 1275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.44', 'subgroup_hash': 44, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245643
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 1276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.44', 'subgroup_hash': 44, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245644
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 1277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245645
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 1278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.32', 'subgroup_hash': 32, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245646
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 1279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.32', 'subgroup_hash': 32, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245648
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 1280, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.33', 'subgroup_hash': 33, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245649
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 1281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.33', 'subgroup_hash': 33, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245650
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 1282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.22', 'subgroup_hash': 22, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:A_4', 'supersolvable': False, 'sylow': 0}
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id: 186245651
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 1283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.22', 'subgroup_hash': 22, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:A_4', 'supersolvable': False, 'sylow': 0}
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id: 186245652
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 1284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.22', 'subgroup_hash': 22, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:A_4', 'supersolvable': False, 'sylow': 0}
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id: 186245653
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 1285, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.22', 'subgroup_hash': 22, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:A_4', 'supersolvable': False, 'sylow': 0}
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id: 186245654
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 27, 'counter': 1286, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.45', 'subgroup_hash': 45, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times C_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186245655
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 1287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.41', 'subgroup_hash': 41, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186245656
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 1288, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.41', 'subgroup_hash': 41, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186245657
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 1289, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186245659
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 1290, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186245660
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 1291, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186245661
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1292, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245662
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.25', 'subgroup_hash': 25, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245663
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 1294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245664
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1295, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.17', 'subgroup_hash': 17, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245665
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 1296, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245666
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1297, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186245667
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 1298, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186245668
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1299, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.17', 'subgroup_hash': 17, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245671
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1300, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.17', 'subgroup_hash': 17, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245672
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 1301, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186245673
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 1302, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245674
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1303, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.28', 'subgroup_hash': 28, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245675
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 1304, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186245676
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 1305, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245677
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 1306, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186245678
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 1307, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186245679
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 1308, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186245680
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 1309, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186245682
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 1310, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186245683
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1311, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.17', 'subgroup_hash': 17, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245684
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 1312, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245685
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 1313, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.17', 'subgroup_hash': 17, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245686
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1314, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.25', 'subgroup_hash': 25, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245687
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 1315, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245688
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 1316, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245689
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 1317, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245690
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 1318, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245691
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 1319, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245693
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1320, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.17', 'subgroup_hash': 17, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245694
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 1321, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.17', 'subgroup_hash': 17, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245695
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 1322, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245696
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1323, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245697
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 1324, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245698
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 1325, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245699
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1326, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.288.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.17', 'subgroup_hash': 17, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245700
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1327, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245701
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1328, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.215', 'subgroup_hash': 215, 'subgroup_order': 96, 'subgroup_tex': 'D_4:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245702
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1329, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245704
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1330, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.215', 'subgroup_hash': 215, 'subgroup_order': 96, 'subgroup_tex': 'D_4:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245705
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1331, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.216', 'subgroup_hash': 216, 'subgroup_order': 96, 'subgroup_tex': 'D_4:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245706
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1332, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.211', 'subgroup_hash': 211, 'subgroup_order': 96, 'subgroup_tex': 'D_4:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245707
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1333, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.211', 'subgroup_hash': 211, 'subgroup_order': 96, 'subgroup_tex': 'D_4:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245708
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1334, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.216', 'subgroup_hash': 216, 'subgroup_order': 96, 'subgroup_tex': 'D_4:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245709
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1335, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245710
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1336, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245711
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1337, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245712
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1338, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245713
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1339, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245715
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1340, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245716
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1341, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245717
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1342, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.87', 'subgroup_hash': 87, 'subgroup_order': 96, 'subgroup_tex': 'D_6.D_4', 'supersolvable': True, 'sylow': 0}
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id: 186245718
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1343, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.87', 'subgroup_hash': 87, 'subgroup_order': 96, 'subgroup_tex': 'D_6.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186245719
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1344, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.87', 'subgroup_hash': 87, 'subgroup_order': 96, 'subgroup_tex': 'D_6.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186245720
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1345, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.87', 'subgroup_hash': 87, 'subgroup_order': 96, 'subgroup_tex': 'D_6.D_4', 'supersolvable': True, 'sylow': 0}
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id: 186245721
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1346, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.87', 'subgroup_hash': 87, 'subgroup_order': 96, 'subgroup_tex': 'D_6.D_4', 'supersolvable': True, 'sylow': 0}
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id: 186245722
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1347, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.87', 'subgroup_hash': 87, 'subgroup_order': 96, 'subgroup_tex': 'D_6.D_4', 'supersolvable': True, 'sylow': 0}
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id: 186245723
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1348, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.87', 'subgroup_hash': 87, 'subgroup_order': 96, 'subgroup_tex': 'D_6.D_4', 'supersolvable': True, 'sylow': 0}
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id: 186245724
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1349, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.224', 'subgroup_hash': 224, 'subgroup_order': 96, 'subgroup_tex': 'C_6.C_2^4', 'supersolvable': True, 'sylow': 0}
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id: 186245726
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1350, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.211', 'subgroup_hash': 211, 'subgroup_order': 96, 'subgroup_tex': 'D_4:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245727
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1351, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.144', 'subgroup_hash': 144, 'subgroup_order': 96, 'subgroup_tex': 'D_6:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186245728
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1352, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.144', 'subgroup_hash': 144, 'subgroup_order': 96, 'subgroup_tex': 'D_6:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186245729
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1353, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.144', 'subgroup_hash': 144, 'subgroup_order': 96, 'subgroup_tex': 'D_6:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186245730
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1354, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.49', 'subgroup_hash': 49, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245731
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1355, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.41', 'subgroup_hash': 41, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245732
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1356, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.41', 'subgroup_hash': 41, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245733
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1357, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.49', 'subgroup_hash': 49, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245734
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1358, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.224', 'subgroup_hash': 224, 'subgroup_order': 96, 'subgroup_tex': 'C_6.C_2^4', 'supersolvable': True, 'sylow': 0}
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id: 186245735
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1359, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.211', 'subgroup_hash': 211, 'subgroup_order': 96, 'subgroup_tex': 'D_4:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245737
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1360, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.89', 'subgroup_hash': 89, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245738
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1361, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.13', 'subgroup_hash': 13, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2.D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245739
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1362, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.13', 'subgroup_hash': 13, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2.D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245740
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1363, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.211', 'subgroup_hash': 211, 'subgroup_order': 96, 'subgroup_tex': 'D_4:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245741
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1364, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.144', 'subgroup_hash': 144, 'subgroup_order': 96, 'subgroup_tex': 'D_6:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186245742
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1365, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.49', 'subgroup_hash': 49, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245743
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1366, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.41', 'subgroup_hash': 41, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245744
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1367, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.89', 'subgroup_hash': 89, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245745
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1368, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.89', 'subgroup_hash': 89, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245746
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1369, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.89', 'subgroup_hash': 89, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245748
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1370, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.13', 'subgroup_hash': 13, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2.D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245749
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1371, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.13', 'subgroup_hash': 13, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2.D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186245750
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1372, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.13', 'subgroup_hash': 13, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2.D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186245751
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1373, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.13', 'subgroup_hash': 13, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2.D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186245752
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1374, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.211', 'subgroup_hash': 211, 'subgroup_order': 96, 'subgroup_tex': 'D_4:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245753
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1375, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.211', 'subgroup_hash': 211, 'subgroup_order': 96, 'subgroup_tex': 'D_4:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245754
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1376, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.144', 'subgroup_hash': 144, 'subgroup_order': 96, 'subgroup_tex': 'D_6:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186245755
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1377, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.144', 'subgroup_hash': 144, 'subgroup_order': 96, 'subgroup_tex': 'D_6:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186245756
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1378, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.49', 'subgroup_hash': 49, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186245757
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1379, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.41', 'subgroup_hash': 41, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245759
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1380, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.89', 'subgroup_hash': 89, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245760
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1381, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.13', 'subgroup_hash': 13, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2.D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245761
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1382, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.144', 'subgroup_hash': 144, 'subgroup_order': 96, 'subgroup_tex': 'D_6:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186245762
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1383, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.89', 'subgroup_hash': 89, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245763
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1384, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.89', 'subgroup_hash': 89, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245764
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1385, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.49', 'subgroup_hash': 49, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245765
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1386, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.41', 'subgroup_hash': 41, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245766
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1387, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.13', 'subgroup_hash': 13, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2.D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245767
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1388, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.13', 'subgroup_hash': 13, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2.D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245768
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1389, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.226', 'subgroup_hash': 226, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times S_4', 'supersolvable': False, 'sylow': 0}
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id: 186245770
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1390, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.194', 'subgroup_hash': 194, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2.S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186245771
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1391, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245772
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1392, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245773
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1393, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245774
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1394, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245775
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1395, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.87', 'subgroup_hash': 87, 'subgroup_order': 96, 'subgroup_tex': 'D_6.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186245776
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1396, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.87', 'subgroup_hash': 87, 'subgroup_order': 96, 'subgroup_tex': 'D_6.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186245777
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1397, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.87', 'subgroup_hash': 87, 'subgroup_order': 96, 'subgroup_tex': 'D_6.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186245778
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1398, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.87', 'subgroup_hash': 87, 'subgroup_order': 96, 'subgroup_tex': 'D_6.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186245779
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1399, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.144', 'subgroup_hash': 144, 'subgroup_order': 96, 'subgroup_tex': 'D_6:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186245782
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1400, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.144', 'subgroup_hash': 144, 'subgroup_order': 96, 'subgroup_tex': 'D_6:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186245783
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1401, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.144', 'subgroup_hash': 144, 'subgroup_order': 96, 'subgroup_tex': 'D_6:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186245784
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1402, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.195', 'subgroup_hash': 195, 'subgroup_order': 96, 'subgroup_tex': '\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
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id: 186245785
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1403, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.89', 'subgroup_hash': 89, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245786
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1404, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.195', 'subgroup_hash': 195, 'subgroup_order': 96, 'subgroup_tex': '\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
-
id: 186245787
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1405, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.144', 'subgroup_hash': 144, 'subgroup_order': 96, 'subgroup_tex': 'D_6:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186245788
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1406, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.89', 'subgroup_hash': 89, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245789
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1407, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.89', 'subgroup_hash': 89, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186245790
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1408, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.89', 'subgroup_hash': 89, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186245791
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 1409, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.228', 'subgroup_hash': 228, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 186245793
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 1410, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.229', 'subgroup_hash': 229, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
-
id: 186245794
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 48, 'counter': 1411, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.230', 'subgroup_hash': 230, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245795
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 1412, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.230', 'subgroup_hash': 230, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245796
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 1413, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.230', 'subgroup_hash': 230, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245797
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 48, 'counter': 1414, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.167', 'subgroup_hash': 167, 'subgroup_order': 96, 'subgroup_tex': 'C_2^4:C_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245798
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 16, 'counter': 1415, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.167', 'subgroup_hash': 167, 'subgroup_order': 96, 'subgroup_tex': 'C_2^4:C_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245799
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 16, 'counter': 1416, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.70', 'subgroup_hash': 70, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
-
id: 186245800
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 16, 'counter': 1417, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.70', 'subgroup_hash': 70, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
-
id: 186245801
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 48, 'counter': 1418, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.160', 'subgroup_hash': 160, 'subgroup_order': 96, 'subgroup_tex': 'C_2^4:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186245802
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 16, 'counter': 1419, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.227', 'subgroup_hash': 227, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186245804
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 48, 'counter': 1420, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.167', 'subgroup_hash': 167, 'subgroup_order': 96, 'subgroup_tex': 'C_2^4:C_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245805
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 16, 'counter': 1421, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.70', 'subgroup_hash': 70, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
-
id: 186245806
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 16, 'counter': 1422, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.70', 'subgroup_hash': 70, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
-
id: 186245807
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 48, 'counter': 1423, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.160', 'subgroup_hash': 160, 'subgroup_order': 96, 'subgroup_tex': 'C_2^4:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186245808
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 16, 'counter': 1424, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.160', 'subgroup_hash': 160, 'subgroup_order': 96, 'subgroup_tex': 'C_2^4:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186245809
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 16, 'counter': 1425, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.227', 'subgroup_hash': 227, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186245810
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 16, 'counter': 1426, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.227', 'subgroup_hash': 227, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186245811
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 16, 'counter': 1427, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.227', 'subgroup_hash': 227, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186245812
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 48, 'counter': 1428, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.167', 'subgroup_hash': 167, 'subgroup_order': 96, 'subgroup_tex': 'C_2^4:C_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245813
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 16, 'counter': 1429, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.167', 'subgroup_hash': 167, 'subgroup_order': 96, 'subgroup_tex': 'C_2^4:C_6', 'supersolvable': True, 'sylow': 0}
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id: 186245815
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 16, 'counter': 1430, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.160', 'subgroup_hash': 160, 'subgroup_order': 96, 'subgroup_tex': 'C_2^4:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186245816
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 16, 'counter': 1431, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.195', 'subgroup_hash': 195, 'subgroup_order': 96, 'subgroup_tex': '\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
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id: 186245817
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 16, 'counter': 1432, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.227', 'subgroup_hash': 227, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186245818
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 16, 'counter': 1433, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.195', 'subgroup_hash': 195, 'subgroup_order': 96, 'subgroup_tex': '\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
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id: 186245819
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 16, 'counter': 1434, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.227', 'subgroup_hash': 227, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186245820
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 16, 'counter': 1435, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.167', 'subgroup_hash': 167, 'subgroup_order': 96, 'subgroup_tex': 'C_2^4:C_6', 'supersolvable': True, 'sylow': 0}
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id: 186245821
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 48, 'counter': 1436, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.160', 'subgroup_hash': 160, 'subgroup_order': 96, 'subgroup_tex': 'C_2^4:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186245822
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 16, 'counter': 1437, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.160', 'subgroup_hash': 160, 'subgroup_order': 96, 'subgroup_tex': 'C_2^4:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186245823
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 1438, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.195', 'subgroup_hash': 195, 'subgroup_order': 96, 'subgroup_tex': '\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
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id: 186245824
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 1439, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.227', 'subgroup_hash': 227, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186245826
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 1440, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.195', 'subgroup_hash': 195, 'subgroup_order': 96, 'subgroup_tex': '\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
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id: 186245827
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 1441, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.ek1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.227', 'subgroup_hash': 227, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186245828
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1442, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.el1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.226', 'subgroup_hash': 226, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times S_4', 'supersolvable': False, 'sylow': 0}
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id: 186245829
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1443, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.em1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.215', 'subgroup_hash': 215, 'subgroup_order': 96, 'subgroup_tex': 'D_4:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245830
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1444, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.en1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.215', 'subgroup_hash': 215, 'subgroup_order': 96, 'subgroup_tex': 'D_4:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245831
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1445, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.eo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.215', 'subgroup_hash': 215, 'subgroup_order': 96, 'subgroup_tex': 'D_4:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245832
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1446, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.ep1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245833
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1447, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.eq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245834
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1448, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.er1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245835
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1449, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.es1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.211', 'subgroup_hash': 211, 'subgroup_order': 96, 'subgroup_tex': 'D_4:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245837
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1450, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.et1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.216', 'subgroup_hash': 216, 'subgroup_order': 96, 'subgroup_tex': 'D_4:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245838
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1451, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.eu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.eu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.211', 'subgroup_hash': 211, 'subgroup_order': 96, 'subgroup_tex': 'D_4:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245839
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1452, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.ev1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.ev1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.216', 'subgroup_hash': 216, 'subgroup_order': 96, 'subgroup_tex': 'D_4:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245840
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1453, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.ew1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.ew1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.211', 'subgroup_hash': 211, 'subgroup_order': 96, 'subgroup_tex': 'D_4:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245841
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1454, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.324.ex1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.ex1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.216', 'subgroup_hash': 216, 'subgroup_order': 96, 'subgroup_tex': 'D_4:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245842
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 1455, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.384.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
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id: 186245843
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 1456, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.384.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
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id: 186245844
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 1457, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.384.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
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id: 186245845
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 1458, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.384.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
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id: 186245846
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 1459, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.384.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
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id: 186245848
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1460, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245849
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1461, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245850
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 1462, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245851
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1463, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245852
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1464, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245853
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1465, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245854
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1466, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245855
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 1467, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.37', 'subgroup_hash': 37, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245856
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 1468, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 186245857
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 1469, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 186245859
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 1470, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 186245860
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1471, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245861
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1472, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.l2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.l2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245862
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1473, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245863
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 1474, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245864
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1475, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245865
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1476, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245866
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1477, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245867
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1478, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245868
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1479, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.r2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.r2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245870
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1480, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245871
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1481, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245872
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 1482, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245873
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1483, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245874
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1484, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245875
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1485, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245876
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1486, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245877
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1487, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
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id: 186245878
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1488, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
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id: 186245879
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1489, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 186245881
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1490, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.35', 'subgroup_hash': 35, 'subgroup_order': 72, 'subgroup_tex': 'C_6^2:C_2', 'supersolvable': True, 'sylow': 0}
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id: 186245882
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1491, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245883
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1492, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245884
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1493, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245885
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1494, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245886
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1495, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245887
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1496, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245888
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 1497, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245889
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1498, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245890
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1499, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245893
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1500, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245894
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1501, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.21', 'subgroup_hash': 21, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245895
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 1502, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.32', 'subgroup_hash': 32, 'subgroup_order': 72, 'subgroup_tex': 'C_{12}:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186245896
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1503, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.21', 'subgroup_hash': 21, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245897
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1504, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.21', 'subgroup_hash': 21, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245898
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 1505, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245899
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1506, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.35', 'subgroup_hash': 35, 'subgroup_order': 72, 'subgroup_tex': 'C_6^2:C_2', 'supersolvable': True, 'sylow': 0}
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id: 186245900
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1507, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.35', 'subgroup_hash': 35, 'subgroup_order': 72, 'subgroup_tex': 'C_6^2:C_2', 'supersolvable': True, 'sylow': 0}
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id: 186245901
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1508, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.22', 'subgroup_hash': 22, 'subgroup_order': 72, 'subgroup_tex': 'D_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186245902
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1509, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.22', 'subgroup_hash': 22, 'subgroup_order': 72, 'subgroup_tex': 'D_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186245904
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1510, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.22', 'subgroup_hash': 22, 'subgroup_order': 72, 'subgroup_tex': 'D_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186245905
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1511, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245906
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1512, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245907
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1513, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245908
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1514, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245909
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1515, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245910
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1516, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245911
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1517, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245912
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1518, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245913
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1519, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245915
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1520, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245916
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1521, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245917
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1522, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245918
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1523, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.21', 'subgroup_hash': 21, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245919
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 1524, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.32', 'subgroup_hash': 32, 'subgroup_order': 72, 'subgroup_tex': 'C_{12}:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186245920
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1525, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.21', 'subgroup_hash': 21, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245921
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1526, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.21', 'subgroup_hash': 21, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245922
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1527, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245923
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1528, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245924
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1529, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245926
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1530, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.33', 'subgroup_hash': 33, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245927
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1531, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245928
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1532, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245929
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1533, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245930
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1534, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.33', 'subgroup_hash': 33, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245931
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1535, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245932
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1536, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245933
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 9, 'counter': 1537, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245934
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1538, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245935
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1539, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245937
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 1540, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.37', 'subgroup_hash': 37, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186245938
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 1541, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
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id: 186245939
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 1542, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
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id: 186245940
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 1543, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
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id: 186245941
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1544, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
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id: 186245942
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1545, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
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id: 186245943
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 1546, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
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id: 186245944
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1547, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.35', 'subgroup_hash': 35, 'subgroup_order': 72, 'subgroup_tex': 'C_6^2:C_2', 'supersolvable': True, 'sylow': 0}
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id: 186245945
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 1548, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.50', 'subgroup_hash': 50, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186245946
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 1549, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245948
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 1550, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245949
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1551, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245950
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1552, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245951
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 1553, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245952
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1554, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245953
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1555, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.do2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.do2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245954
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1556, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245955
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1557, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.dp2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.dp2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245956
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1558, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245957
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1559, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245959
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 1560, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245960
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1561, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186245961
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1562, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245962
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1563, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245963
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1564, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245964
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 1565, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245965
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 1566, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245966
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 1567, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245967
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1568, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245968
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1569, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245970
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 1570, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.36', 'subgroup_hash': 36, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245971
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 1571, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.36', 'subgroup_hash': 36, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245972
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 1572, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.34', 'subgroup_hash': 34, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245973
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 1573, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.34', 'subgroup_hash': 34, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245974
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 1574, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245975
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 1575, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245976
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 1576, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245977
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1577, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245978
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1578, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ek1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245979
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1579, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ek2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ek2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186245981
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 3, 'counter': 1580, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.el1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.50', 'subgroup_hash': 50, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 186245982
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 3, 'counter': 1581, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.em1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.50', 'subgroup_hash': 50, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186245983
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 9, 'counter': 1582, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.en1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.50', 'subgroup_hash': 50, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186245984
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 1583, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.eo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.50', 'subgroup_hash': 50, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186245985
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 1584, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ep1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.50', 'subgroup_hash': 50, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186245986
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1585, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.eq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186245987
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1586, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.er1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245988
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1587, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.es1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186245989
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 1588, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.et1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186245990
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 1589, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.eu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.eu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186245992
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1590, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ev1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ev1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245993
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1591, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ew1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ew1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245994
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1592, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ex1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ex1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186245995
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1593, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ey1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ey1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186245996
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 1594, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ez1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ez1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186245997
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 1595, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.fa1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.fa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186245998
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1596, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.fb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.fb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186245999
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 9, 'counter': 1597, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.fc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.fc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246000
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1598, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.fd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.fd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246001
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1599, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.fe1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.fe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186246004
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 1600, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ff1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ff1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.37', 'subgroup_hash': 37, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186246005
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 1601, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.fg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.fg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 186246006
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 1602, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.fh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.fh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 186246007
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 1603, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.fi1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.fi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186246008
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 1604, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.fj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.fj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186246009
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 1605, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.fk1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.fk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246010
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 1606, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.fl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.fl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 186246011
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 1607, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.fm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.fm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186246012
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 1608, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.fn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.fn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246013
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 1609, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.fn2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.fn2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186246015
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 1610, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.fo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.fo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
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id: 186246016
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 1611, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.fp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.fp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
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id: 186246017
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1612, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.fq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.fq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
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id: 186246018
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1613, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.fr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.fr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 186246019
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1614, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.fs1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.fs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246020
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1615, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ft1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ft1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246021
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 1616, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.fu1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.fu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246022
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 1617, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.fv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.fv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186246023
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1618, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.fw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.fw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 186246024
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1619, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.fx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.fx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
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id: 186246026
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1620, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.fy1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.fy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246027
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1621, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.fz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.fz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246028
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 1622, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ga1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ga1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246029
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 1623, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.gb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.gb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246030
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1624, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.gc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.gc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246031
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1625, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.gd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.gd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246032
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1626, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ge1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ge1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246033
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1627, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.gf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.gf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246034
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1628, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.gg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.gg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246035
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 1629, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.gh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.gh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246037
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1630, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.gi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.gi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246038
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1631, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.gj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.gj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246039
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1632, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.gj2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.gj2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246040
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1633, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.gk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.gk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
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id: 186246041
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1634, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.gl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.gl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
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id: 186246042
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1635, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.gm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.gm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
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id: 186246043
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1636, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.gn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.gn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.35', 'subgroup_hash': 35, 'subgroup_order': 72, 'subgroup_tex': 'C_6^2:C_2', 'supersolvable': True, 'sylow': 0}
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id: 186246044
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1637, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.go1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.go1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186246045
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 1638, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.gp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.gp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246046
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 1639, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.gq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.gq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246048
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 1640, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.gr1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.gr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246049
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1641, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.gs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.gs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.35', 'subgroup_hash': 35, 'subgroup_order': 72, 'subgroup_tex': 'C_6^2:C_2', 'supersolvable': True, 'sylow': 0}
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id: 186246050
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1642, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.gt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.gt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.35', 'subgroup_hash': 35, 'subgroup_order': 72, 'subgroup_tex': 'C_6^2:C_2', 'supersolvable': True, 'sylow': 0}
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id: 186246051
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1643, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.gu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.gu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.35', 'subgroup_hash': 35, 'subgroup_order': 72, 'subgroup_tex': 'C_6^2:C_2', 'supersolvable': True, 'sylow': 0}
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id: 186246052
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1644, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.gv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.gv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246053
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1645, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.gw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.gw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246054
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1646, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.gx1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.gx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246055
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1647, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.gy1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.gy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246056
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1648, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.gz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.gz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.35', 'subgroup_hash': 35, 'subgroup_order': 72, 'subgroup_tex': 'C_6^2:C_2', 'supersolvable': True, 'sylow': 0}
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id: 186246057
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1649, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ha1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ha1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246059
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1650, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.hb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.hb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246060
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1651, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.hc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.hc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246061
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1652, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.hd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.hd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246062
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1653, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.he1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.he1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246063
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1654, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.hf1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.hf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246064
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1655, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.hg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.hg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246065
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1656, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.hh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.hh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246066
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1657, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.hi1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.hi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246067
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1658, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.hj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.hj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246068
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1659, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.hj2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.hj2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246070
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 3, 'counter': 1660, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.hk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.hk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.50', 'subgroup_hash': 50, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186246071
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 1661, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.hl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.hl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246072
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 1662, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.hm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.hm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246073
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 9, 'counter': 1663, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.hn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.hn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.50', 'subgroup_hash': 50, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186246074
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 1664, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ho1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ho1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.50', 'subgroup_hash': 50, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186246075
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 1665, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.hp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.hp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.50', 'subgroup_hash': 50, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186246076
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 1666, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.hq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.hq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.50', 'subgroup_hash': 50, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186246077
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 1667, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.hr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.hr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246078
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 1668, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.hs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.hs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246079
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 1669, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ht1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ht1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246081
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 1670, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.hu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.hu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246082
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 1671, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.hv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.hv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246083
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 1672, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.hw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.hw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246084
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1673, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.hx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.hx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246085
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1674, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.hy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.hy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246086
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1675, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.hz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.hz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246087
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 1676, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ia1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ia1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246088
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 1677, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ib1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ib1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246089
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1678, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ic1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ic1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246090
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1679, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.id1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.id1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246092
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1680, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ie1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ie1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.32', 'subgroup_hash': 32, 'subgroup_order': 72, 'subgroup_tex': 'C_{12}:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246093
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1681, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.if1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.if1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.21', 'subgroup_hash': 21, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246094
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1682, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ig1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ig1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.21', 'subgroup_hash': 21, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246095
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1683, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ih1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ih1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.21', 'subgroup_hash': 21, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246096
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 1684, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ii1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ii1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.21', 'subgroup_hash': 21, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246097
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 1685, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ij1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ij1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.32', 'subgroup_hash': 32, 'subgroup_order': 72, 'subgroup_tex': 'C_{12}:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246098
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1686, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ik1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ik1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.21', 'subgroup_hash': 21, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246099
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1687, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.il1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.il1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246100
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1688, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.im1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.im1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
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id: 186246101
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1689, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.in1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.in1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246103
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1690, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.io1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.io1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
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id: 186246104
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1691, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ip1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ip1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.35', 'subgroup_hash': 35, 'subgroup_order': 72, 'subgroup_tex': 'C_6^2:C_2', 'supersolvable': True, 'sylow': 0}
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id: 186246105
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1692, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.iq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.iq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.35', 'subgroup_hash': 35, 'subgroup_order': 72, 'subgroup_tex': 'C_6^2:C_2', 'supersolvable': True, 'sylow': 0}
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id: 186246106
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1693, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ir1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ir1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
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id: 186246107
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1694, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.is1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.is1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186246108
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1695, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.it1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.it1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186246109
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1696, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.iu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.iu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246110
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1697, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.iv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.iv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246111
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1698, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.iw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.iw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246112
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1699, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ix1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ix1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246115
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1700, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.iy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.iy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.28', 'subgroup_hash': 28, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246116
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1701, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.iz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.iz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246117
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1702, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ja1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ja1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246118
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1703, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.jb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.jb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
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id: 186246119
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1704, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.jc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.jc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.22', 'subgroup_hash': 22, 'subgroup_order': 72, 'subgroup_tex': 'D_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246120
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1705, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.jd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.jd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246121
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1706, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.je1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.je1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246122
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 1707, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.jf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.jf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246123
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1708, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.jg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.jg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246124
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1709, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.jh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.jh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246126
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1710, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ji1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ji1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246127
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1711, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.jj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.jj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.28', 'subgroup_hash': 28, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186246128
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1712, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.jk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.jk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186246129
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1713, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.jl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.jl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186246130
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1714, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.jm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.jm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186246131
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1715, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.jn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.jn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186246132
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1716, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.jo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.jo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186246133
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1717, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.jp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.jp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186246134
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1718, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.jq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.jq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 186246135
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1719, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.jr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.jr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186246137
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1720, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.js1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.js1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.22', 'subgroup_hash': 22, 'subgroup_order': 72, 'subgroup_tex': 'D_6:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186246138
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1721, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.jt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.jt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 186246139
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1722, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ju1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ju1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.28', 'subgroup_hash': 28, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186246140
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1723, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.jv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.jv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186246141
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1724, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.jw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.jw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186246142
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 1725, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.jx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.jx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186246143
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1726, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.jy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.jy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186246144
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1727, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.jz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.jz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186246145
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1728, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ka1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ka1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246146
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1729, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.kb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.kb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.22', 'subgroup_hash': 22, 'subgroup_order': 72, 'subgroup_tex': 'D_6:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186246148
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1730, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.kc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.kc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186246149
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1731, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.kd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.kd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186246150
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1732, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ke1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ke1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186246151
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1733, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.kf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.kf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186246152
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1734, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.kg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.kg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246153
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1735, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.kh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.kh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246154
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1736, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ki1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ki1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.22', 'subgroup_hash': 22, 'subgroup_order': 72, 'subgroup_tex': 'D_6:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186246155
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1737, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.kj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.kj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246156
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1738, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.kk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.kk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.33', 'subgroup_hash': 33, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246157
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1739, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.kl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.kl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.33', 'subgroup_hash': 33, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186246159
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1740, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.km1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.km1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246160
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1741, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.kn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.kn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.21', 'subgroup_hash': 21, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246161
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1742, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ko1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ko1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.21', 'subgroup_hash': 21, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246162
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1743, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.kp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.kp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246163
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1744, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.kq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.kq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246164
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 1745, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.kr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.kr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246165
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1746, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ks1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ks1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.35', 'subgroup_hash': 35, 'subgroup_order': 72, 'subgroup_tex': 'C_6^2:C_2', 'supersolvable': True, 'sylow': 0}
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id: 186246166
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1747, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.kt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.kt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246167
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1748, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ku1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ku1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246168
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1749, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.kv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.kv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186246170
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1750, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.kw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.kw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186246171
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1751, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.kw2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.kw2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186246172
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1752, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.kx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.kx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186246173
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1753, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ky1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ky1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246174
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1754, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.kz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.kz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246175
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1755, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.la1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.la1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.21', 'subgroup_hash': 21, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186246176
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 1756, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.lb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.lb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.32', 'subgroup_hash': 32, 'subgroup_order': 72, 'subgroup_tex': 'C_{12}:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246177
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1757, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.lc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.lc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.21', 'subgroup_hash': 21, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246178
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1758, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ld1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ld1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246179
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1759, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ld2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ld2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246181
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1760, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.le1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.le1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246182
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1761, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.lf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.lf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.33', 'subgroup_hash': 33, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246183
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1762, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.lg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.lg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.32', 'subgroup_hash': 32, 'subgroup_order': 72, 'subgroup_tex': 'C_{12}:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246184
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1763, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.lh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.lh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.21', 'subgroup_hash': 21, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246185
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1764, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.li1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.li1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.21', 'subgroup_hash': 21, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246186
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1765, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.lj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.lj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.21', 'subgroup_hash': 21, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246187
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1766, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.lk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.lk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246188
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1767, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ll1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ll1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246189
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1768, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.lm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.lm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.21', 'subgroup_hash': 21, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246190
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1769, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ln1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ln1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.21', 'subgroup_hash': 21, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186246192
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1770, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.lo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.lo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.26', 'subgroup_hash': 26, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 186246193
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1771, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.lp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.lp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.24', 'subgroup_hash': 24, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 186246194
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1772, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.lq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.lq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.26', 'subgroup_hash': 26, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 186246195
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1773, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.lr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.lr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.24', 'subgroup_hash': 24, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
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id: 186246196
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1774, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ls1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ls1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.26', 'subgroup_hash': 26, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
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id: 186246197
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1775, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.lt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.lt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.24', 'subgroup_hash': 24, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
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id: 186246198
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1776, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.lu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.lu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.24', 'subgroup_hash': 24, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
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id: 186246199
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1777, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.lv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.lv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 186246200
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1778, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.lw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.lw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246201
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1779, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.lx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.lx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246203
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1780, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ly1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ly1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186246204
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 1781, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.lz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.lz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246205
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1782, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ma1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ma1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246206
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 1783, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.mb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.mb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246207
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1784, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.mc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.mc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246208
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 1785, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.md1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.md1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.37', 'subgroup_hash': 37, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186246209
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 1786, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.me1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.me1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.50', 'subgroup_hash': 50, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186246210
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1787, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.mf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.mf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246211
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1788, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.mg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.mg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246212
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 1789, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.mh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.mh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 186246214
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 1790, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.mi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.mi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
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id: 186246215
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1791, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.mj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.mj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246216
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 1792, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.mk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.mk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
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id: 186246217
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 1793, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ml1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ml1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246218
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1794, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.mm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.mm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246219
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 1795, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.mn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.mn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246220
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 1796, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.mo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.mo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246221
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1797, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.mp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.mp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246222
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1798, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.mq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.mq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246223
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 1799, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.mr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.mr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
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id: 186246226
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1800, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ms1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ms1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
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id: 186246227
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1801, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.mt1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.mt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246228
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 1802, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.mu1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.mu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246229
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1803, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.mv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.mv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246230
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 1804, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.mv2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.mv2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246231
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1805, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.mw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.mw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
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id: 186246232
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1806, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.mx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.mx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246233
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1807, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.my1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.my1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246234
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 1808, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.mz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.mz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 186246235
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1809, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.na1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.na1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186246237
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1810, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.nb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.nb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.35', 'subgroup_hash': 35, 'subgroup_order': 72, 'subgroup_tex': 'C_6^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 186246238
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1811, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.nc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.nc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186246239
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 1812, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.nd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.nd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186246240
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 1813, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ne1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ne1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186246241
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 1814, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.nf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.nf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.37', 'subgroup_hash': 37, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186246242
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 1815, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ng1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ng1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 186246243
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 1816, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.nh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.nh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 186246244
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 1817, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ni1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ni1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186246245
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 1818, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.nj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.nj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186246246
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 1819, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.nk1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.nk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186246248
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 1820, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.nk2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.nk2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186246249
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 1821, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.nl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.nl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 186246250
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 1822, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.nm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.nm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186246251
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 1823, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.nn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.nn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186246252
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1824, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.no1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.no1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186246253
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1825, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.no2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.no2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186246254
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1826, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.np1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.np1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186246255
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1827, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.nq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.nq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186246256
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 1828, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.nr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.nr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186246257
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1829, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ns1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ns1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186246259
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1830, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ns2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ns2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246260
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1831, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.nt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.nt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 186246261
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 1832, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.nu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.nu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
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id: 186246262
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1833, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.nv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.nv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 186246263
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1834, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.nw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.nw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186246264
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1835, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.nx1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.nx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186246265
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 1836, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ny1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ny1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246266
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1837, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.nz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.nz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.35', 'subgroup_hash': 35, 'subgroup_order': 72, 'subgroup_tex': 'C_6^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 186246267
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1838, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.oa1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.oa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186246268
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 1839, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ob1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ob1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.36', 'subgroup_hash': 36, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246270
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 1840, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.oc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.oc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246271
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 1841, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.od1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.od1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186246272
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1842, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.oe1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.oe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246273
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1843, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.oe2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.oe2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186246274
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 1844, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.of1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.of1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.34', 'subgroup_hash': 34, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186246275
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 1845, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.og1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.og1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186246276
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1846, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.oh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.oh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186246277
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1847, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.oi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.oi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186246278
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1848, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.oj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.oj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186246279
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1849, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ok1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ok1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186246281
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1850, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.ol1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ol1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186246282
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1851, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.om1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.om1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186246283
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1852, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.on1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.on1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186246284
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1853, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.432.oo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.oo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186246285
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1854, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.486.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '486.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.90', 'subgroup_hash': 90, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 186246286
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1855, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.486.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '486.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.264', 'subgroup_hash': 264, 'subgroup_order': 64, 'subgroup_tex': 'D_4:C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 186246287
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1856, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.486.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '486.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.90', 'subgroup_hash': 90, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 186246288
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1857, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.486.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '486.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.138', 'subgroup_hash': 138, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186246289
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1858, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.486.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '486.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.138', 'subgroup_hash': 138, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186246290
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1859, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.486.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '486.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.138', 'subgroup_hash': 138, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186246292
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 1860, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.486.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '486.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186246293
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 1861, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.486.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '486.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186246294
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 16, 'counter': 1862, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.486.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '486.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.138', 'subgroup_hash': 138, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186246295
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 16, 'counter': 1863, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.486.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '486.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.138', 'subgroup_hash': 138, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186246296
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 1864, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.486.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '486.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.138', 'subgroup_hash': 138, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186246297
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 54, 'counter': 1865, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '31104.fx.576.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '576.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '576.8654', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8654, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 576, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '\\POPlus(4,3)', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186246298
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 27, 'counter': 1866, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186246299
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 1867, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186246300
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 1868, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186246301
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 1869, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.10', 'subgroup_hash': 10, 'subgroup_order': 54, 'subgroup_tex': 'C_2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
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id: 186246303
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 1870, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.10', 'subgroup_hash': 10, 'subgroup_order': 54, 'subgroup_tex': 'C_2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
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id: 186246304
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 1871, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.10', 'subgroup_hash': 10, 'subgroup_order': 54, 'subgroup_tex': 'C_2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
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id: 186246305
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 1872, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.10', 'subgroup_hash': 10, 'subgroup_order': 54, 'subgroup_tex': 'C_2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
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id: 186246306
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 27, 'counter': 1873, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186246307
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 1874, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186246308
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 1875, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186246309
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1876, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
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id: 186246310
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 1877, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
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id: 186246311
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 1878, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
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id: 186246312
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1879, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
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id: 186246314
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1880, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.10', 'subgroup_hash': 10, 'subgroup_order': 54, 'subgroup_tex': 'C_2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
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id: 186246315
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 1881, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186246316
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 1882, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186246317
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 1883, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186246318
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 1884, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186246319
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1885, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
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id: 186246320
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 1886, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
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id: 186246321
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 1887, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
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id: 186246322
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 1888, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
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id: 186246323
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 1889, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186246325
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 1890, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186246326
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 1891, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186246327
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1892, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246328
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1893, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
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id: 186246329
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 1894, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246330
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 1895, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
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id: 186246331
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 1896, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
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id: 186246332
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 1897, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
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id: 186246333
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 1898, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
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id: 186246334
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 1899, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
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id: 186246337
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 1900, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
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id: 186246338
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 1901, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
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id: 186246339
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 1902, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
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id: 186246340
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 1903, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186246341
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 1904, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186246342
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 1905, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186246343
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 1906, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186246344
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 1907, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186246345
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 1908, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246346
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 1909, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
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id: 186246348
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 1910, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246349
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1911, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246350
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 1912, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246351
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 1913, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
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id: 186246352
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1914, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
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id: 186246353
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1915, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
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id: 186246354
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1916, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.by2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.by2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
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id: 186246355
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 1917, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246356
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 1918, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186246357
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1919, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
-
id: 186246359
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 1920, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
-
id: 186246360
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 1921, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
-
id: 186246361
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1922, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
-
id: 186246362
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1923, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
-
id: 186246363
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 1924, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186246364
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 1925, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186246365
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1926, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186246366
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 1927, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186246367
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1928, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186246368
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1929, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.576.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186246370
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 48, 'counter': 1930, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '31104.fx.648.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '648.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '648.555', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 555, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 648, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3.S_3^3', 'simple': False, 'solvable': True, 'special_labels': ['C7', 'C7'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.52', 'subgroup_hash': 52, 'subgroup_order': 48, 'subgroup_tex': 'C_2^3\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186246371
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1931, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246372
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1932, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186246373
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1933, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186246374
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1934, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246375
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1935, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246376
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1936, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186246377
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1937, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186246378
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1938, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186246379
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1939, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186246381
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1940, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186246382
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1941, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186246383
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1942, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186246384
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1943, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186246385
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1944, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186246386
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1945, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186246387
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1946, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186246388
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1947, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186246389
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1948, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186246390
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1949, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186246392
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1950, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186246393
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1951, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186246394
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1952, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186246395
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1953, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246396
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1954, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.47', 'subgroup_hash': 47, 'subgroup_order': 48, 'subgroup_tex': 'D_4:C_6', 'supersolvable': True, 'sylow': 0}
-
id: 186246397
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1955, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186246398
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1956, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246399
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1957, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186246400
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1958, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186246401
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1959, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.39', 'subgroup_hash': 39, 'subgroup_order': 48, 'subgroup_tex': 'D_4:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186246403
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1960, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186246404
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1961, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.47', 'subgroup_hash': 47, 'subgroup_order': 48, 'subgroup_tex': 'D_4:C_6', 'supersolvable': True, 'sylow': 0}
-
id: 186246405
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1962, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186246406
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1963, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186246407
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1964, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.37', 'subgroup_hash': 37, 'subgroup_order': 48, 'subgroup_tex': 'D_{12}:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 186246408
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1965, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186246409
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1966, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.39', 'subgroup_hash': 39, 'subgroup_order': 48, 'subgroup_tex': 'D_4:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246410
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1967, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186246411
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1968, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.39', 'subgroup_hash': 39, 'subgroup_order': 48, 'subgroup_tex': 'D_4:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246412
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1969, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246414
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1970, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.37', 'subgroup_hash': 37, 'subgroup_order': 48, 'subgroup_tex': 'D_{12}:C_2', 'supersolvable': True, 'sylow': 0}
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id: 186246415
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1971, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246416
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1972, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246417
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1973, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.bq2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.bq2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246418
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1974, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246419
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1975, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246420
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1976, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246421
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1977, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246422
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1978, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246423
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1979, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186246425
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1980, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246426
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1981, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246427
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1982, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186246428
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1983, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186246429
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1984, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186246430
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1985, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.cb2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.cb2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186246431
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1986, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 186246432
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1987, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186246433
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1988, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186246434
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1989, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186246436
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1990, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246437
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1991, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246438
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1992, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246439
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1993, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186246440
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1994, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186246441
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1995, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186246442
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1996, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186246443
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1997, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246444
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1998, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186246445
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1999, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246449
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2000, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246450
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2001, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246451
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 2002, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246452
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2003, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246453
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2004, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246454
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 2005, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246455
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 2006, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246456
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 2007, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246457
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2008, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246458
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2009, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246460
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 2010, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246461
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2011, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246462
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2012, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246463
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2013, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246464
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2014, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246465
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2015, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246466
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2016, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246467
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2017, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186246468
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2018, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246469
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 2019, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246471
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2020, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246472
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 2021, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.21', 'subgroup_hash': 21, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246473
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 2022, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246474
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 2023, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.21', 'subgroup_hash': 21, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246475
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 2024, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.21', 'subgroup_hash': 21, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246476
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 2025, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246477
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 2026, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246478
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2027, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.21', 'subgroup_hash': 21, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246479
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2028, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246480
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2029, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.21', 'subgroup_hash': 21, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246482
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2030, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.21', 'subgroup_hash': 21, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246483
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2031, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246484
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2032, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246485
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2033, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246486
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2034, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.21', 'subgroup_hash': 21, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246487
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2035, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246488
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2036, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186246489
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2037, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246490
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2038, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246491
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2039, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246493
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2040, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246494
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2041, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246495
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2042, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246496
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2043, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246497
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2044, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246498
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2045, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246499
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2046, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.ek1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246500
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2047, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.el1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246501
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2048, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.em1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246502
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2049, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.en1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246504
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2050, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.eo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246505
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2051, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.ep1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246506
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2052, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.eq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186246507
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 2053, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.er1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186246508
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2054, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.es1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186246509
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2055, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.et1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186246510
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2056, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.eu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.eu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246511
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2057, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.ev1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ev1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246512
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2058, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.ew1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ew1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246513
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2059, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.ex1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ex1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246515
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2060, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.ey1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ey1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246516
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2061, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.ez1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ez1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246517
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2062, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.fa1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.fa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246518
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2063, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.fb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.fb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246519
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2064, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.fc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.fc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246520
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2065, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.fd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.fd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246521
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 2066, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.fe1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.fe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246522
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2067, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.ff1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ff1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246523
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2068, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.fg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.fg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246524
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2069, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.fh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.fh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246526
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2070, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.fi1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.fi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246527
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 2071, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.fj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.fj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.21', 'subgroup_hash': 21, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246528
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 2072, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.fk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.fk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246529
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2073, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.fl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.fl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.21', 'subgroup_hash': 21, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246530
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2074, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.fm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.fm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.21', 'subgroup_hash': 21, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246531
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2075, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.fn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.fn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246532
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2076, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.fo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.fo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246533
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2077, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.fp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.fp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246534
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2078, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.fq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.fq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.21', 'subgroup_hash': 21, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246535
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2079, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.fr1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.fr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.30', 'subgroup_hash': 30, 'subgroup_order': 48, 'subgroup_tex': 'A_4:C_4', 'supersolvable': False, 'sylow': 0}
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id: 186246537
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2080, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.fs1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.fs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.30', 'subgroup_hash': 30, 'subgroup_order': 48, 'subgroup_tex': 'A_4:C_4', 'supersolvable': False, 'sylow': 0}
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id: 186246538
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2081, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.ft1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ft1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.30', 'subgroup_hash': 30, 'subgroup_order': 48, 'subgroup_tex': 'A_4:C_4', 'supersolvable': False, 'sylow': 0}
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id: 186246539
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2082, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.fu1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.fu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.30', 'subgroup_hash': 30, 'subgroup_order': 48, 'subgroup_tex': 'A_4:C_4', 'supersolvable': False, 'sylow': 0}
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id: 186246540
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 16, 'counter': 2083, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.fv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.fv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.52', 'subgroup_hash': 52, 'subgroup_order': 48, 'subgroup_tex': 'C_2^3\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186246541
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 16, 'counter': 2084, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.fw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.fw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.52', 'subgroup_hash': 52, 'subgroup_order': 48, 'subgroup_tex': 'C_2^3\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186246542
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 16, 'counter': 2085, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.fx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.fx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246543
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 16, 'counter': 2086, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.fy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.fy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.50', 'subgroup_hash': 50, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246544
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 16, 'counter': 2087, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.fz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.fz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246545
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 16, 'counter': 2088, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.ga1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ga1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.50', 'subgroup_hash': 50, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246546
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 16, 'counter': 2089, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.gb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.gb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246548
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 16, 'counter': 2090, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.gc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.gc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.50', 'subgroup_hash': 50, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246549
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2091, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.gd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.gd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246550
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2092, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.ge1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ge1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246551
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2093, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.gf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.gf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186246552
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2094, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.gg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.gg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246553
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2095, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.gh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.gh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246554
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2096, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.gi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.gi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246555
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2097, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.gj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.gj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246556
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2098, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.gk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.gk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246557
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2099, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.gl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.gl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246560
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.gm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.gm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246561
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.gn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.gn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246562
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.go1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.go1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246563
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.gp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.gp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.40', 'subgroup_hash': 40, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
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id: 186246564
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.gq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.gq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.40', 'subgroup_hash': 40, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
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id: 186246565
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.gr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.gr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246566
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.gs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.gs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.39', 'subgroup_hash': 39, 'subgroup_order': 48, 'subgroup_tex': 'D_4:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246567
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.gt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.gt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246568
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.gu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.gu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.37', 'subgroup_hash': 37, 'subgroup_order': 48, 'subgroup_tex': 'D_{12}:C_2', 'supersolvable': True, 'sylow': 0}
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id: 186246569
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.gv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.gv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246571
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.gw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.gw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246572
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.gx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.gx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246573
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.gy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.gy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186246574
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.gz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.gz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.39', 'subgroup_hash': 39, 'subgroup_order': 48, 'subgroup_tex': 'D_4:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246575
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.ha1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ha1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.37', 'subgroup_hash': 37, 'subgroup_order': 48, 'subgroup_tex': 'D_{12}:C_2', 'supersolvable': True, 'sylow': 0}
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id: 186246576
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.hb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.hb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.39', 'subgroup_hash': 39, 'subgroup_order': 48, 'subgroup_tex': 'D_4:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246577
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.hc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.hc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.37', 'subgroup_hash': 37, 'subgroup_order': 48, 'subgroup_tex': 'D_{12}:C_2', 'supersolvable': True, 'sylow': 0}
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id: 186246578
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.hd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.hd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246579
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.he1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.he1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246580
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.hf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.hf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246582
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.hg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.hg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.39', 'subgroup_hash': 39, 'subgroup_order': 48, 'subgroup_tex': 'D_4:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246583
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.hh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.hh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246584
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.hi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.hi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.41', 'subgroup_hash': 41, 'subgroup_order': 48, 'subgroup_tex': 'D_{12}:C_2', 'supersolvable': True, 'sylow': 0}
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id: 186246585
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.hj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.hj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246586
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.hk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.hk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246587
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.hl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.hl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.37', 'subgroup_hash': 37, 'subgroup_order': 48, 'subgroup_tex': 'D_{12}:C_2', 'supersolvable': True, 'sylow': 0}
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id: 186246588
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.hm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.hm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.41', 'subgroup_hash': 41, 'subgroup_order': 48, 'subgroup_tex': 'D_{12}:C_2', 'supersolvable': True, 'sylow': 0}
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id: 186246589
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.hn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.hn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246590
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.ho1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ho1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246591
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.hp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.hp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246593
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.hq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.hq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246594
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.hr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.hr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186246595
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.hs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.hs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.37', 'subgroup_hash': 37, 'subgroup_order': 48, 'subgroup_tex': 'D_{12}:C_2', 'supersolvable': True, 'sylow': 0}
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id: 186246596
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.ht1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ht1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.39', 'subgroup_hash': 39, 'subgroup_order': 48, 'subgroup_tex': 'D_4:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246597
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.hu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.hu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.37', 'subgroup_hash': 37, 'subgroup_order': 48, 'subgroup_tex': 'D_{12}:C_2', 'supersolvable': True, 'sylow': 0}
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id: 186246598
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.hv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.hv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.37', 'subgroup_hash': 37, 'subgroup_order': 48, 'subgroup_tex': 'D_{12}:C_2', 'supersolvable': True, 'sylow': 0}
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id: 186246599
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.hw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.hw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.41', 'subgroup_hash': 41, 'subgroup_order': 48, 'subgroup_tex': 'D_{12}:C_2', 'supersolvable': True, 'sylow': 0}
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id: 186246600
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.hx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.hx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.37', 'subgroup_hash': 37, 'subgroup_order': 48, 'subgroup_tex': 'D_{12}:C_2', 'supersolvable': True, 'sylow': 0}
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id: 186246601
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.hy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.hy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.41', 'subgroup_hash': 41, 'subgroup_order': 48, 'subgroup_tex': 'D_{12}:C_2', 'supersolvable': True, 'sylow': 0}
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id: 186246602
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.hz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.hz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246604
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.ia1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ia1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.37', 'subgroup_hash': 37, 'subgroup_order': 48, 'subgroup_tex': 'D_{12}:C_2', 'supersolvable': True, 'sylow': 0}
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id: 186246605
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.ib1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ib1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246606
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.ic1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ic1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.41', 'subgroup_hash': 41, 'subgroup_order': 48, 'subgroup_tex': 'D_{12}:C_2', 'supersolvable': True, 'sylow': 0}
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id: 186246607
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.id1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.id1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246608
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.ie1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ie1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246609
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.if1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.if1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246610
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.ig1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ig1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246611
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.ih1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ih1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246612
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.ii1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ii1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246613
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.ij1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ij1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246615
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.ik1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ik1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246616
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.il1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.il1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246617
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.im1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.im1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246618
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.in1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.in1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246619
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.in2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.in2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246620
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.io1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.io1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246621
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.ip1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ip1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246622
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.iq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.iq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246623
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.ir1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ir1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246624
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.is1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.is1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246626
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.it1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.it1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186246627
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 2161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.iu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.iu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246628
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.iv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.iv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246629
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.iw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.iw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246630
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.ix1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ix1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246631
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.iy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.iy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246632
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 2166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.iz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.iz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.47', 'subgroup_hash': 47, 'subgroup_order': 48, 'subgroup_tex': 'D_4:C_6', 'supersolvable': True, 'sylow': 0}
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id: 186246633
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.ja1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ja1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.39', 'subgroup_hash': 39, 'subgroup_order': 48, 'subgroup_tex': 'D_4:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246634
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.jb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.jb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.47', 'subgroup_hash': 47, 'subgroup_order': 48, 'subgroup_tex': 'D_4:C_6', 'supersolvable': True, 'sylow': 0}
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id: 186246635
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 2169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.jc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.jc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.39', 'subgroup_hash': 39, 'subgroup_order': 48, 'subgroup_tex': 'D_4:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186246637
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 2170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.jd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.jd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246638
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.je1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.je1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246639
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.jf1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.jf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246640
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.jg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.jg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246641
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.jh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.jh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246642
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.ji1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ji1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246643
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.ji2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ji2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246644
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.jj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.jj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246645
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.jk1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.jk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246646
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 2179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.jl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.jl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246648
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 2180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.jm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.jm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.39', 'subgroup_hash': 39, 'subgroup_order': 48, 'subgroup_tex': 'D_4:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246649
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.jn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.jn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246650
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 2182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.jo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.jo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.37', 'subgroup_hash': 37, 'subgroup_order': 48, 'subgroup_tex': 'D_{12}:C_2', 'supersolvable': True, 'sylow': 0}
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id: 186246651
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 2183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.jp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.jp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246652
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.jq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.jq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
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id: 186246653
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 2185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.jr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.jr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246654
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.js1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.js1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246655
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 2187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.jt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.jt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186246656
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 2188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.ju1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.ju1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.47', 'subgroup_hash': 47, 'subgroup_order': 48, 'subgroup_tex': 'D_4:C_6', 'supersolvable': True, 'sylow': 0}
-
id: 186246657
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.jv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.jv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.39', 'subgroup_hash': 39, 'subgroup_order': 48, 'subgroup_tex': 'D_4:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186246659
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.jw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.jw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186246660
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 2191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.jx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.jx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.39', 'subgroup_hash': 39, 'subgroup_order': 48, 'subgroup_tex': 'D_4:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186246661
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.jy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.jy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.37', 'subgroup_hash': 37, 'subgroup_order': 48, 'subgroup_tex': 'D_{12}:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 186246662
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.jz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.jz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.39', 'subgroup_hash': 39, 'subgroup_order': 48, 'subgroup_tex': 'D_4:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186246663
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.ka1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ka1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.37', 'subgroup_hash': 37, 'subgroup_order': 48, 'subgroup_tex': 'D_{12}:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 186246664
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.kb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.kb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186246665
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.kc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.kc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186246666
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.kd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.kd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186246667
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.ke1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ke1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186246668
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.kf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.kf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186246671
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.kg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.kg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186246672
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.kh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.kh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186246673
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.ki1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ki1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186246674
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.kj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.kj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186246675
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.kj2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.kj2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186246676
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.kk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.kk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186246677
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.kl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.kl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186246678
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.km1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.km1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 186246679
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.kn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.kn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186246680
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.ko1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ko1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186246682
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.kp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.kp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186246683
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.648.kp2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.kp2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186246684
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 3, 'counter': 2212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186246685
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 3, 'counter': 2213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186246686
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 9, 'counter': 2214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186246687
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 2215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186246688
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 2216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186246689
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 2217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186246690
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 2218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186246691
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 2219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246693
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246694
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246695
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246696
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 9, 'counter': 2223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246697
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246698
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246699
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186246700
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 2227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186246701
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 2228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246702
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 2229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246704
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 2230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246705
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246706
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246707
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246708
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246709
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246710
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246711
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 2237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246712
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246713
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246715
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246716
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.bc2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.bc2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246717
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 9, 'counter': 2242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246718
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246719
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246720
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246721
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.bg2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.bg2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246722
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246723
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 9, 'counter': 2248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246724
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246726
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246727
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246728
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246729
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.bm2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.bm2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246730
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 2254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246731
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246732
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246733
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246734
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.bq2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.bq2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246735
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 2259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246737
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246738
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246739
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 2262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246740
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 2263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246741
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186246742
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246743
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246744
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 2267, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246745
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 2268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246746
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 2269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246748
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 2270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186246749
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 2271, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246750
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 2272, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246751
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 2273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186246752
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2274, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246753
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246754
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246755
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246756
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246757
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186246759
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2280, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246760
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186246761
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186246762
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186246763
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246764
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 3, 'counter': 2285, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186246765
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 3, 'counter': 2286, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186246766
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': False, 'core_order': 9, 'counter': 2287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186246767
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 2288, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186246768
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 2289, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186246770
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 3, 'counter': 2290, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186246771
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 2291, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186246772
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 2292, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246773
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 2293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246774
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 2294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246775
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 2295, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246776
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 2296, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186246777
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 2297, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246778
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 2298, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246779
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 2299, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.de2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.de2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246782
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1296, 'characteristic': False, 'core_order': 9, 'counter': 2300, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186246783
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 2301, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186246784
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 2302, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 186246785
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 2303, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186246786
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 2304, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186246787
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 2305, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246788
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 2306, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246789
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 2307, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246790
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 2308, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246791
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 2309, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186246793
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 2310, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246794
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 2311, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186246795
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 2312, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186246796
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2313, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246797
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2314, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246798
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 2315, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246799
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 2316, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246800
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 2317, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246801
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 2318, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246802
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 2319, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246804
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 2320, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246805
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 2321, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 186246806
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 2322, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246807
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 2323, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246808
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 2324, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246809
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 2325, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246810
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 2326, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.ee2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ee2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246811
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 2327, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246812
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2328, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246813
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 9, 'counter': 2329, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246815
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2330, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246816
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2331, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246817
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 2332, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.ek1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186246818
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 2333, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.el1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246819
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 2334, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.em1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246820
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 2335, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.en1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246821
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2336, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.eo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246822
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 2337, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.ep1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246823
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 2338, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.eq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246824
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2339, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.er1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246826
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 2340, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.es1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 186246827
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 2341, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.et1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246828
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2342, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.eu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.eu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246829
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2343, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.ev1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ev1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246830
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2344, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.ew1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ew1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246831
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2345, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.ew2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ew2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246832
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 2346, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.ex1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ex1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246833
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2347, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.ey1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ey1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246834
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2348, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.ey2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ey2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246835
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2349, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.ez1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ez1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246837
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2350, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.ez2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ez2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246838
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2351, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.ez3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ez3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246839
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2352, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.fa1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.fa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246840
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2353, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.fb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.fb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246841
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 9, 'counter': 2354, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.fc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.fc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246842
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2355, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.fd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.fd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246843
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2356, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.fe1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.fe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246844
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2357, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.ff1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ff1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246845
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 2358, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.ff2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ff2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246846
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2359, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.fg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.fg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186246848
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2360, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.fg2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.fg2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246849
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 2361, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.fh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.fh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246850
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2362, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.fi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.fi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246851
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2363, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.fj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.fj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246852
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2364, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.fk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.fk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246853
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2365, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.fl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.fl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246854
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 2366, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.fm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.fm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246855
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 2367, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.fn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.fn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246856
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 2368, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.fo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.fo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246857
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 2369, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.fp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.fp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246859
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 2370, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.fq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.fq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246860
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2371, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.fr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.fr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246861
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 2372, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.fs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.fs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246862
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2373, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.ft1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ft1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186246863
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2374, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.fu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.fu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246864
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 2375, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.fv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.fv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246865
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 2376, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.fw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.fw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246866
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 2377, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.fx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.fx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246867
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 2378, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.fy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.fy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 186246868
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2379, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.fz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.fz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246870
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2380, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.ga1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ga1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186246871
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 3, 'counter': 2381, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.gb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.gb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186246872
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': False, 'core_order': 3, 'counter': 2382, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.gc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.gc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186246873
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 3, 'counter': 2383, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.gd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.gd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186246874
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 2384, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.ge1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ge1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246875
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 2385, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.gf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.gf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246876
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 2386, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.gg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.gg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246877
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 2387, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.gh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.gh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246878
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 2388, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.gh2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.gh2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246879
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 2389, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.gh3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.gh3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246881
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 9, 'counter': 2390, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.gi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.gi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186246882
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 2391, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.gj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.gj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
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id: 186246883
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 2392, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.gk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.gk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246884
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 2393, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.gl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.gl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186246885
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2394, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.gm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.gm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246886
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2395, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.gn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.gn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246887
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 2396, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.go1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.go1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246888
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 2397, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.gp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.gp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186246889
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 2398, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.gq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.gq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186246890
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 2399, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.gr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.gr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186246893
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 2400, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.gs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.gs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186246894
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 2401, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.gt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.gt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186246895
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 2402, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.gu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.gu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186246896
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2403, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.gv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.gv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186246897
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2404, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.gw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.gw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186246898
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 2405, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.gx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.gx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186246899
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2406, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.gy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.gy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246900
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2407, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.gz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.gz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186246901
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 2408, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.ha1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ha1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186246902
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 2409, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.hb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.hb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246904
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2410, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.hc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.hc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186246905
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2411, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.hd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.hd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186246906
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 2412, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.he1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.he1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246907
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 2413, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.hf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.hf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246908
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 2414, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.hg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.hg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246909
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2415, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.hh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.hh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246910
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 2416, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.hi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.hi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186246911
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 2417, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.hj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.hj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246912
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2418, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.hk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.hk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186246913
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2419, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.hl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.hl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186246915
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2420, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.hl2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.hl2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186246916
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 2421, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.hm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.hm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186246917
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 2422, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.hn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.hn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186246918
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 2423, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.ho1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ho1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186246919
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 2424, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.hp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.hp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186246920
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 2425, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.hq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.hq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246921
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 2426, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.hr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.hr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186246922
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 2427, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.hs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.hs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186246923
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2428, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.ht1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ht1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186246924
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 2429, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.hu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.hu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186246926
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 2430, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.hv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.hv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186246927
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 2431, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.hw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.hw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246928
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 2432, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.hx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.hx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186246929
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 2433, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.hy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.hy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186246930
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 2434, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.hz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.hz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186246931
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2435, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.ia1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ia1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186246932
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 2436, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.ib1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ib1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186246933
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 2437, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.ic1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ic1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186246934
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 2438, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.id1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.id1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186246935
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 2439, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.ie1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ie1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246937
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2440, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.if1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.if1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186246938
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 2441, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.ig1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ig1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246939
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 2442, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.ih1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ih1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186246940
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 2443, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.ii1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ii1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186246941
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2444, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.ij1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ij1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186246942
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2445, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.ik1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ik1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186246943
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2446, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.il1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.il1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186246944
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2447, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.im1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.im1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186246945
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2448, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.im2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.im2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186246946
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2449, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.in1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.in1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186246948
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2450, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.864.io1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.io1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186246949
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2451, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.972.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246950
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2452, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.972.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 186246951
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2453, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.972.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 186246952
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2454, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.972.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186246953
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2455, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.972.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246954
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2456, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.972.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246955
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2457, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.972.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186246956
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2458, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.972.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186246957
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2459, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.972.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 186246959
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2460, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.972.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
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id: 186246960
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2461, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.972.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186246961
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2462, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.972.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186246962
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2463, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.972.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 186246963
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2464, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.972.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
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id: 186246964
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2465, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.972.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186246965
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2466, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.972.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186246966
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2467, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.972.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 186246967
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2468, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.972.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
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id: 186246968
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2469, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.972.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186246970
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2470, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.972.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
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id: 186246971
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2471, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.972.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186246972
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2472, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.972.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186246973
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2473, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.972.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186246974
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2474, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.972.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186246975
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2475, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.972.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
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id: 186246976
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2476, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.972.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
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id: 186246977
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 2477, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.972.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
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id: 186246978
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 16, 'counter': 2478, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.972.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
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id: 186246979
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 16, 'counter': 2479, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.972.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
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id: 186246981
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 16, 'counter': 2480, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.972.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
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id: 186246982
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 16, 'counter': 2481, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.972.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
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id: 186246983
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2482, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.972.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 186246984
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2483, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.972.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186246985
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2484, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.972.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 186246986
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2485, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.972.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 186246987
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': True, 'core_order': 27, 'counter': 2486, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '31104.fx.1152.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1152.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '1152.157852', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4208954026111918128, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 1152, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'A_4^2:C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
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id: 186246988
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 2487, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1152.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1152.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
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id: 186246989
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 2488, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1152.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1152.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
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id: 186246990
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 2489, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1152.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1152.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
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id: 186246992
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 2490, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1152.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1152.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
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id: 186246993
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 2491, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1152.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1152.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
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id: 186246994
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 2492, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1152.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1152.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
-
id: 186246995
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 9, 'counter': 2493, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1152.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1152.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
-
id: 186246996
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 2494, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1152.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1152.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
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id: 186246997
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 2495, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1152.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1152.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
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id: 186246998
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 2496, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1152.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1152.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
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id: 186246999
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2497, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1152.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1152.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
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id: 186247000
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2498, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1152.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1152.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
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id: 186247001
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 2499, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1152.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1152.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
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id: 186247004
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 2500, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1152.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1152.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
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id: 186247005
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 2501, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1152.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1152.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
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id: 186247006
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 2502, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1152.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1152.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
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id: 186247007
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2503, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247008
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2504, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247009
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2505, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247010
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2506, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247011
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2507, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247012
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2508, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247013
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2509, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247015
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 2510, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247016
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2511, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186247017
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2512, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247018
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2513, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247019
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2514, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247020
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2515, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247021
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2516, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247022
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2517, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247023
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2518, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247024
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2519, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.p2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.p2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247026
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2520, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247027
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2521, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247028
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2522, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.r2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.r2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247029
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2523, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247030
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2524, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247031
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2525, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247032
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2526, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247033
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2527, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247034
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2528, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247035
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2529, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247037
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2530, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186247038
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 2531, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247039
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2532, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247040
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2533, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247041
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2534, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247042
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2535, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247043
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2536, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247044
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2537, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247045
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2538, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247046
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2539, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247048
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2540, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247049
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2541, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247050
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2542, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247051
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2543, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247052
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2544, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247053
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2545, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247054
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2546, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247055
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2547, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247056
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2548, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247057
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2549, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186247059
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2550, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247060
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2551, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247061
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2552, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247062
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2553, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247063
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2554, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247064
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2555, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186247065
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2556, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186247066
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2557, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247067
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2558, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247068
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2559, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247070
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2560, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247071
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2561, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247072
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2562, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247073
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2563, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186247074
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2564, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186247075
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2565, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186247076
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2566, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247077
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2567, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186247078
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2568, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186247079
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2569, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186247081
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 2570, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247082
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2571, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247083
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2572, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247084
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2573, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247085
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2574, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247086
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 2575, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247087
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2576, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247088
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2577, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247089
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 2578, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247090
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2579, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247092
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2580, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247093
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2581, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247094
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2582, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247095
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 2583, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247096
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2584, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247097
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2585, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247098
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2586, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247099
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2587, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247100
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2588, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.de2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.de2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247101
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2589, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247103
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2590, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247104
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2591, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.dg2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.dg2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247105
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2592, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247106
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2593, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247107
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2594, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247108
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2595, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247109
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2596, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247110
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2597, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247111
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2598, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247112
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2599, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247115
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2600, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247116
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 2601, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186247117
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 2602, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186247118
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2603, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247119
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2604, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247120
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2605, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186247121
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2606, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186247122
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2607, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186247123
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2608, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 186247124
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2609, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 186247126
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2610, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.dy2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.dy2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 186247127
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2611, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 186247128
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2612, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 186247129
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2613, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186247130
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2614, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186247131
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 3, 'counter': 2615, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247132
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 2616, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247133
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 2617, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247134
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 2618, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247135
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 2619, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247137
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2620, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247138
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2621, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186247139
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2622, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ek1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186247140
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 2623, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.el1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247141
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2624, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.em1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247142
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2625, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.en1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247143
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2626, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.eo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247144
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 2627, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ep1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186247145
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2628, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.eq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186247146
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2629, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.er1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186247148
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2630, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.es1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247149
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2631, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.et1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247150
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2632, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.eu1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.eu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
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id: 186247151
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2633, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ev1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ev1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
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id: 186247152
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2634, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ew1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ew1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247153
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2635, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ex1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ex1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
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id: 186247154
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 2636, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ey1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ey1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
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id: 186247155
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2637, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ez1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ez1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186247156
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2638, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.fa1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.fa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247157
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2639, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.fb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.fb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247159
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2640, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.fc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.fc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247160
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2641, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.fd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.fd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247161
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2642, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.fd2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.fd2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247162
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2643, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.fe1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.fe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186247163
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 2644, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ff1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ff1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186247164
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2645, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.fg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.fg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186247165
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2646, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.fh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.fh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186247166
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2647, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.fi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.fi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186247167
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2648, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.fj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.fj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186247168
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2649, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.fk1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.fk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186247170
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2650, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.fl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.fl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247171
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2651, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.fm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.fm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186247172
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 2652, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.fn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.fn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186247173
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 3, 'counter': 2653, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.fo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.fo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247174
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 2654, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.fp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.fp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247175
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 2655, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.fq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.fq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247176
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 2656, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.fr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.fr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247177
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 2657, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.fs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.fs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247178
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2658, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ft1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ft1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 186247179
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2659, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.fu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.fu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 186247181
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2660, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.fv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.fv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 186247182
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2661, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.fw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.fw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 186247183
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2662, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.fx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.fx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247184
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2663, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.fy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.fy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247185
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2664, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.fz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.fz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247186
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2665, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ga1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ga1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247187
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2666, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.gb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.gb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247188
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2667, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.gc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.gc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247189
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2668, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.gd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.gd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247190
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2669, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ge1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ge1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186247192
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2670, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.gf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.gf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186247193
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2671, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.gg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.gg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186247194
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2672, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.gh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.gh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186247195
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2673, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.gi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.gi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186247196
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2674, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.gj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.gj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186247197
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2675, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.gk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.gk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186247198
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2676, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.gl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.gl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247199
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2677, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.gm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.gm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186247200
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2678, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.gn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.gn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247201
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2679, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.go1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.go1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247203
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2680, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.gp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.gp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247204
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2681, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.gq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.gq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247205
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2682, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.gr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.gr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186247206
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2683, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.gs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.gs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247207
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2684, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.gt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.gt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247208
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2685, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.gu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.gu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247209
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2686, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.gv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.gv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247210
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2687, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.gw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.gw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247211
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2688, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.gx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.gx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247212
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2689, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.gy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.gy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247214
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2690, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.gz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.gz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247215
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2691, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ha1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.ha1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247216
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2692, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.hb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.hb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247217
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2693, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.hc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.hc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247218
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2694, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.hd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.hd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186247219
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2695, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.he1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.he1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186247220
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2696, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.hf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.hf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247221
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2697, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.hg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.hg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247222
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2698, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.hh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.hh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247223
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2699, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.hi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.hi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247226
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2700, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.hj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.hj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247227
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2701, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.hk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.hk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186247228
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2702, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.hl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.hl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186247229
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2703, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.hm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.hm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186247230
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2704, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.hn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.hn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186247231
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2705, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ho1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ho1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186247232
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2706, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.hp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.hp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247233
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2707, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.hq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.hq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247234
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2708, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.hr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.hr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247235
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2709, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.hs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.hs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247237
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2710, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ht1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.ht1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247238
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2711, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.hu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.hu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186247239
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2712, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.hv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.hv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247240
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2713, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.hw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.hw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247241
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2714, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.hx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.hx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186247242
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2715, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.hy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.hy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 186247243
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2716, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.hz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.hz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247244
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2717, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ia1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ia1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186247245
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2718, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ib1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ib1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186247246
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2719, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ic1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ic1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186247248
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2720, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.id1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.id1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186247249
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2721, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ie1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ie1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186247250
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2722, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.if1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.if1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186247251
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2723, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ig1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ig1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186247252
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2724, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ih1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ih1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247253
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2725, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ii1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ii1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186247254
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2726, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ij1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ij1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247255
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2727, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ik1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ik1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247256
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2728, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.il1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.il1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247257
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2729, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.im1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.im1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247259
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2730, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.in1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.in1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247260
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2731, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.io1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.io1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247261
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2732, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ip1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ip1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247262
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2733, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.iq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.iq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186247263
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2734, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ir1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ir1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247264
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2735, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.is1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.is1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247265
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2736, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.it1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.it1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247266
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2737, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.it2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.it2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247267
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2738, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.iu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.iu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247268
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2739, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.iv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.iv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186247270
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2740, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.iw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.iw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 186247271
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2741, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ix1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ix1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247272
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2742, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.iy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.iy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186247273
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2743, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.iz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.iz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186247274
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2744, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ja1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ja1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186247275
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2745, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.jb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.jb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186247276
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2746, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.jc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.jc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186247277
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2747, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.jd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.jd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247278
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2748, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.je1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.je1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186247279
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2749, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.je2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.je2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186247281
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2750, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.jf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.jf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186247282
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2751, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.jg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.jg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247283
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2752, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.jh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.jh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186247284
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2753, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ji1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ji1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186247285
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2754, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.jj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.jj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186247286
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2755, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.jk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.jk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186247287
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2756, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.jl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.jl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 186247288
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2757, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.jm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.jm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186247289
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2758, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.jn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.jn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186247290
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2759, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.jo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.jo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.11', 'subgroup_hash': 11, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 186247292
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2760, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.jp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.jp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 186247293
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2761, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.jq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.jq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 186247294
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2762, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.jr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.jr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 186247295
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2763, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.js1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.js1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 186247296
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2764, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.jt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.jt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.11', 'subgroup_hash': 11, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 186247297
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2765, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ju1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ju1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 186247298
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2766, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.jv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.jv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186247299
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 2767, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.jw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.jw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247300
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 2768, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.jw2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.jw2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247301
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2769, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.jx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.jx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247303
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2770, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.jy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.jy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247304
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2771, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.jz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.jz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247305
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 2772, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ka1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.ka1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247306
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2773, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.kb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.kb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247307
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2774, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.kc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.kc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247308
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 2775, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.kd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.kd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247309
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2776, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ke1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.ke1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247310
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2777, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.kf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.kf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186247311
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2778, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.kg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.kg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186247312
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 2779, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.kh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.kh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247314
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2780, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ki1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ki1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
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id: 186247315
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 2781, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.kj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.kj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247316
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2782, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.kk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.kk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247317
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2783, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.kl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.kl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247318
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2784, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.km1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.km1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186247319
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2785, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.kn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.kn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 186247320
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2786, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ko1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ko1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247321
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2787, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.kp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.kp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247322
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2788, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.kq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.kq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247323
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2789, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.kr1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.kr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
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id: 186247325
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2790, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ks1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ks1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
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id: 186247326
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2791, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.kt1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.kt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
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id: 186247327
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 2792, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.kt2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.kt2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
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id: 186247328
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2793, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ku1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ku1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247329
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2794, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.kv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.kv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247330
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 2795, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.kw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.kw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247331
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 2796, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.kw2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.kw2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186247332
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2797, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.kx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.kx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186247333
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2798, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ky1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ky1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186247334
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2799, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.kz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.kz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186247337
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2800, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.la1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.la1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186247338
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2801, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.lb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.lb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247339
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2802, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.lb2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.lb2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247340
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2803, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.lc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.lc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247341
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2804, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ld1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ld1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247342
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2805, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ld2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ld2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247343
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2806, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.le1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.le1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247344
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2807, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.le2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.le2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247345
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2808, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.lf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.lf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186247346
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2809, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.lg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.lg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186247348
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2810, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.lg2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.lg2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186247349
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2811, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.lh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.lh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186247350
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2812, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.li1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.li1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186247351
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2813, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.lj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.lj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
-
id: 186247352
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 2814, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.lk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.lk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186247353
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 2815, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ll1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ll1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 186247354
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2816, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.lm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.lm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186247355
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2817, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ln1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ln1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247356
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2818, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.lo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.lo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 186247357
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2819, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.lp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.lp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186247359
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2820, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.lq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.lq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247360
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2821, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.lq2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.lq2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247361
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2822, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.lr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.lr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247362
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2823, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.ls1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ls1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247363
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2824, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.lt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.lt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247364
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2825, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.lu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.lu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247365
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2826, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1296.lv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.lv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247366
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 3, 'counter': 2827, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247367
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 2828, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247368
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 2829, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247370
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2592, 'characteristic': False, 'core_order': 9, 'counter': 2830, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247371
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 2831, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247372
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 2832, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247373
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 2833, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247374
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 2834, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247375
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 2835, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247376
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 2836, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247377
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 2837, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247378
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 2838, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247379
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 2839, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247381
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': False, 'core_order': 3, 'counter': 2840, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247382
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 3, 'counter': 2841, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247383
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': False, 'core_order': 9, 'counter': 2842, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247384
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 2843, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247385
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 2844, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247386
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2845, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247387
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 2846, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247388
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 2847, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247389
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 2848, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186247390
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2849, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186247392
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2850, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186247393
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 2851, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186247394
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 2852, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186247395
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 9, 'counter': 2853, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186247396
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2854, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186247397
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 2855, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247398
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 2856, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247399
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 2857, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247400
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 2858, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247401
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 2859, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247403
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 2860, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247404
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 2861, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247405
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 9, 'counter': 2862, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247406
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2863, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247407
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 2864, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247408
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 2865, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247409
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 2866, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247410
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2867, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247411
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 2868, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247412
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 2869, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247414
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 2870, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247415
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 2871, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247416
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 2872, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247417
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 2873, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247418
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2874, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247419
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 2875, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247420
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 2876, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247421
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 2877, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247422
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 2878, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247423
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2879, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247425
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 2880, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247426
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 2881, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247427
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 2882, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247428
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 2883, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247429
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 2884, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247430
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 2885, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247431
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 2886, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247432
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 2887, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247433
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 2888, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247434
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 2889, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.cj2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.cj2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247436
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2890, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247437
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2891, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247438
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2892, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247439
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 2893, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247440
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2894, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247441
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2895, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.co2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.co2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247442
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 2896, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247443
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2897, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247444
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 2898, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247445
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2899, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247448
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2900, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247449
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2901, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247450
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 9, 'counter': 2902, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247451
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2903, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247452
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2904, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.cw2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.cw2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247453
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2905, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.cw3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.cw3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247454
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2906, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247455
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 2907, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.cx2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.cx2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247456
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 9, 'counter': 2908, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247457
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2909, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247459
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2910, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.cz2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.cz2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186247460
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2911, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247461
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2912, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247462
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 2913, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247463
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 2914, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247464
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 2915, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247465
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 2916, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247466
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 2917, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247467
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2918, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247468
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2919, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247470
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 2920, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247471
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2921, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247472
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 2922, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247473
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 2923, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247474
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2924, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247475
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 2925, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247476
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 2926, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247477
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 2927, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247478
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 2928, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247479
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 2929, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1728.dr2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1728.dr2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 186247481
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': True, 'core_order': 16, 'counter': 2930, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '31104.fx.1944.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '1944.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '1944.2342', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 2342, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 1944, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2.S_3^3', 'simple': False, 'solvable': True, 'special_labels': ['C8', 'C8'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 186247482
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2931, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186247483
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2932, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186247484
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2933, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247485
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2934, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 186247486
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2935, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247487
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2936, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 186247488
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2937, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247489
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2938, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247490
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2939, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
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id: 186247492
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2940, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247493
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2941, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
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id: 186247494
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2942, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247495
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2943, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
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id: 186247496
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2944, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247497
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2945, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247498
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2946, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247499
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2947, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247500
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2948, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 186247501
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2949, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247503
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2950, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247504
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2951, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
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id: 186247505
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2952, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247506
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2953, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247507
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2954, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247508
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2955, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
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id: 186247509
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2956, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247510
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2957, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247511
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2958, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247512
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2959, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247514
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2960, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247515
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2961, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247516
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2962, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247517
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2963, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
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id: 186247518
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2964, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247519
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2965, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
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id: 186247520
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2966, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247521
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2967, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247522
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2968, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247523
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2969, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247525
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2970, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247526
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2971, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
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id: 186247527
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2972, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247528
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2973, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247529
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2974, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
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id: 186247530
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2975, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247531
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2976, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
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id: 186247532
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2977, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247533
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2978, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247534
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2979, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
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id: 186247536
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2980, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
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id: 186247537
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2981, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247538
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2982, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247539
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2983, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247540
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2984, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
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id: 186247541
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2985, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
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id: 186247542
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2986, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
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id: 186247543
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2987, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247544
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2988, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
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id: 186247545
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2989, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247547
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2990, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
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id: 186247548
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2991, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247549
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2992, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247550
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2993, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247551
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2994, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247552
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2995, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
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id: 186247553
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2996, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
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id: 186247554
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2997, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247555
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2998, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247556
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2999, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247560
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3000, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
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id: 186247561
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3001, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
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id: 186247562
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3002, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247563
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3003, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247564
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3004, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247565
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3005, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.1944.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247566
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 3, 'counter': 3006, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247567
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 3007, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247568
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 3008, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247569
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 3009, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247571
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 3010, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247572
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 3011, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247573
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 3012, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247574
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3013, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247575
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 3014, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247576
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3015, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247577
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3016, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247578
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3017, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247579
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3018, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247580
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 3019, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247582
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 3020, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247583
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 3021, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247584
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 3022, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247585
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 3023, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247586
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 3024, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247587
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3025, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247588
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 3026, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247589
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3027, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247590
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3028, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247591
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3029, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247593
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3030, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.x2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.x2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247594
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3031, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247595
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3032, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.y2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.y2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247596
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 3033, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247597
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3034, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247598
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3035, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247599
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3036, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247600
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3037, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247601
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 3038, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247602
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3039, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247604
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3040, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247605
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3041, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247606
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3042, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.bh2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.bh2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247607
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3043, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247608
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3044, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.bi2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.bi2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247609
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3045, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247610
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 3046, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247611
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3047, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247612
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3048, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247613
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 3049, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247615
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 3050, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247616
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 3051, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186247617
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 3052, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247618
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 3053, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186247619
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 3054, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186247620
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3055, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247621
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3056, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247622
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 3057, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247623
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3058, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186247624
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 3059, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247626
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 3060, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247627
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 3061, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247628
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 3062, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247629
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': False, 'core_order': 3, 'counter': 3063, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247630
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': False, 'core_order': 1, 'counter': 3064, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247631
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': False, 'core_order': 1, 'counter': 3065, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247632
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 3066, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247633
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 3067, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247634
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1296, 'characteristic': False, 'core_order': 3, 'counter': 3068, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247635
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1296, 'characteristic': False, 'core_order': 1, 'counter': 3069, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247637
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1296, 'characteristic': False, 'core_order': 1, 'counter': 3070, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247638
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 3071, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247639
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 3072, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247640
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 3073, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
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id: 186247641
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 3074, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
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id: 186247642
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 3075, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247643
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 3076, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
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id: 186247644
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 3077, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
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id: 186247645
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 3078, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247646
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 3079, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
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id: 186247648
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 3080, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
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id: 186247649
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 3, 'counter': 3081, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247650
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3082, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247651
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 3083, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247652
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3084, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247653
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3085, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247654
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 3086, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247655
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3087, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247656
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 3088, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247657
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 3089, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247659
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 3090, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247660
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 3091, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247661
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3092, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247662
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3093, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247663
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 3094, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247664
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 3095, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247665
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3096, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247666
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 3097, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247667
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3098, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247668
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3099, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.dk2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.dk2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247671
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247672
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247673
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.dm2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.dm2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247674
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247675
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.dn2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.dn2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247676
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.dn3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.dn3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247677
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 3106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247678
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247679
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247680
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247682
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247683
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 3111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247684
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 3112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.dt2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.dt2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247685
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247686
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247687
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247688
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.dw2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.dw2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247689
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247690
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247691
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 3119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247693
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247694
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 3121, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186247695
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 3122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247696
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 3123, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186247697
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 3124, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186247698
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 3125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247699
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 3126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247700
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 3127, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186247701
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247702
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3129, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186247704
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 3130, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.ek1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186247705
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.el1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247706
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.em1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247707
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.en1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247708
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3134, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.eo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 186247709
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': False, 'core_order': 3, 'counter': 3135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.ep1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247710
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': False, 'core_order': 3, 'counter': 3136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.ep2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.ep2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247711
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 3137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.eq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247712
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': False, 'core_order': 1, 'counter': 3138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.er1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247713
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 3139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.es1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247715
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 3140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.et1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
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id: 186247716
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 3141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.eu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.eu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
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id: 186247717
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 3142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.ev1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.ev1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
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id: 186247718
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 3143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.ev2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.ev2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
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id: 186247719
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 3144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.ew1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.ew1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247720
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 3145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.ex1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.ex1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247721
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 3146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.ey1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.ey1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247722
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 3147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.ez1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.ez1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247723
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 3148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.fa1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.fa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247724
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.fb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.fb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247726
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 3150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.fc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.fc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247727
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 3151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.fd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.fd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247728
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.fe1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.fe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247729
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.ff1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.ff1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247730
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 3154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.fg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.fg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247731
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.fh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.fh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247732
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 3156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.fi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.fi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247733
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 3157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.fj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.fj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247734
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 3158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.fk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.fk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247735
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.fl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.fl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247737
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.fl2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.fl2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247738
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.fm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.fm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247739
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 3162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.fn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.fn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247740
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 3163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.fo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.fo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247741
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 3164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.fp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.fp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247742
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 3165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.fq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.fq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247743
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 3166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.fr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.fr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247744
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 3167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.fs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.fs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247745
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 3168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.ft1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.ft1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247746
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 3169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.fu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.fu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247748
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.fv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.fv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247749
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 3171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.fw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.fw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247750
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.fx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.fx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247751
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.fx2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.fx2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247752
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 3174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.fy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.fy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247753
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.fz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.fz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247754
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 3176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.ga1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.ga1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247755
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.gb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.gb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247756
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.2592.gc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.gc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 186247757
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 7776, 'characteristic': True, 'core_order': 9, 'counter': 3179, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '31104.fx.3456.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '3456.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '3456.di', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 9016919946097627263, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 3456, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^4:S_3^3', 'simple': False, 'solvable': True, 'special_labels': ['Phi', 'Phi'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186247759
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': False, 'core_order': 3, 'counter': 3180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3456.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3456.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3456, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186247760
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 3, 'counter': 3181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3456.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3456.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3456, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186247761
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 3, 'counter': 3182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3456.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3456.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3456, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186247762
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 3, 'counter': 3183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3456.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3456.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3456, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186247763
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 3184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3456.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3456.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3456, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186247764
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 3185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3456.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3456.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3456, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186247765
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 3186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3456.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3456.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3456, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186247766
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 3187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3456.h2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3456.h2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3456, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186247767
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 3188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3456.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3456.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3456, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186247768
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 3189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3456.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3456.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3456, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186247770
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 3190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3456.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3456.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3456, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186247771
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 3191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3456.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3456.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3456, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186247772
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 3192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3456.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3456.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3456, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186247773
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 3193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3456.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3456.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3456, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186247774
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 3194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3456.n2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3456.n2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3456, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186247775
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 3195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3456.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3456.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3456, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 186247776
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 3196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3456.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3456.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3456, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186247777
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 3197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3456.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3456.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3456, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186247778
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 3198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3456.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3456.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3456, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186247779
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 3199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3456.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3456.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3456, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186247782
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 3200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3456.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3456.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3456, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186247783
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 3201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3456.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3456.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3456, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186247784
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 3202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3456.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3456.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3456, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186247785
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 3203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3456.v2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3456.v2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3456, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
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id: 186247786
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 186247787
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 3205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247788
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 186247789
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 186247790
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247791
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 186247793
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247794
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 186247795
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247796
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247797
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247798
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247799
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247800
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 3217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 186247801
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247802
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247804
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 186247805
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 186247806
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 186247807
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 186247808
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247809
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247810
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247811
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247812
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': False, 'core_order': 1, 'counter': 3228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 186247813
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 186247815
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 3230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247816
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 186247817
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247818
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': False, 'core_order': 1, 'counter': 3233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 186247819
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 186247820
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 186247821
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247822
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247823
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 186247824
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 186247826
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247827
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247828
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247829
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247830
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247831
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247832
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247833
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 186247834
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247835
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247837
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247838
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247839
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247840
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247841
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247842
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 186247843
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247844
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 186247845
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247846
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247848
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247849
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247850
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247851
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247852
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247853
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
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id: 186247854
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
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id: 186247855
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3267, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
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id: 186247856
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 3268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 186247857
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247859
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 186247860
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3271, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
-
id: 186247861
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3272, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 186247862
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247863
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3274, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 186247864
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
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id: 186247865
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247866
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247867
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 186247868
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.3888.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 186247870
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2592, 'characteristic': False, 'core_order': 3, 'counter': 3280, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247871
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2592, 'characteristic': False, 'core_order': 1, 'counter': 3281, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247872
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2592, 'characteristic': False, 'core_order': 1, 'counter': 3282, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247873
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': False, 'core_order': 1, 'counter': 3283, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247874
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 3284, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247875
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 3285, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247876
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 3286, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247877
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 3287, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247878
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 3288, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247879
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1728, 'characteristic': False, 'core_order': 3, 'counter': 3289, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247881
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': False, 'core_order': 1, 'counter': 3290, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
-
id: 186247882
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1728, 'characteristic': False, 'core_order': 1, 'counter': 3291, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247883
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': False, 'core_order': 1, 'counter': 3292, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247884
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 3293, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247885
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 3294, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247886
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 3295, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247887
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': False, 'core_order': 3, 'counter': 3296, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5184.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247888
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 3297, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5184.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247889
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 3298, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5184.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247890
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 3, 'counter': 3299, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247893
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3300, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247894
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 3301, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247895
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 3302, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247896
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 3, 'counter': 3303, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5184.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247897
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 3304, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5184.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247898
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 3305, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247899
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 3306, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247900
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 3307, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247901
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 3308, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5184.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247902
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3309, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5184.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247904
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 3310, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5184.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247905
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 3311, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5184.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247906
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 3312, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5184.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247907
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 3313, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247908
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 3314, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247909
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3315, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5184.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247910
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 3316, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5184.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247911
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 3317, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5184.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247912
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 3318, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5184.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247913
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 3319, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5184.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247915
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3320, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247916
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 3321, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5184.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247917
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3322, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5184.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247918
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3323, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.bq2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5184.bq2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247919
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3324, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5184.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247920
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3325, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.br2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5184.br2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247921
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 3, 'counter': 3326, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5184.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247922
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3327, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5184.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247923
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3328, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5184.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247924
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3329, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.bu2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5184.bu2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247926
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 3330, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.bu3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5184.bu3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247927
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3331, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
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id: 186247928
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 3332, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5184.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247929
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3333, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5184.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247930
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 3334, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5184.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247931
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 3335, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5184.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247932
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 3336, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5184.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247933
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 3337, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.5184.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5184.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
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id: 186247934
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': False, 'core_order': 1, 'counter': 3338, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.7776.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 186247935
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 3339, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.7776.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 186247937
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3340, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.7776.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 186247938
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 3341, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.7776.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 186247939
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3342, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.7776.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 186247940
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3343, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.7776.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 186247941
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3344, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.7776.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 186247942
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3345, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.7776.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247943
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3346, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.7776.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247944
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1728, 'characteristic': False, 'core_order': 1, 'counter': 3347, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.7776.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 186247945
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2592, 'characteristic': False, 'core_order': 1, 'counter': 3348, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.7776.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 186247946
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 3349, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.7776.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 186247948
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 3350, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.7776.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 186247949
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3351, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.7776.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 186247950
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 3352, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.7776.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 186247951
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3353, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.7776.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 186247952
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 3354, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.7776.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 186247953
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 3355, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.7776.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 186247954
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3356, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.7776.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 186247955
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 3357, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.7776.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247956
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 3358, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.7776.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247957
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3359, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.7776.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247959
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3360, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.7776.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
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id: 186247960
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1728, 'characteristic': False, 'core_order': 1, 'counter': 3361, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.7776.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 186247961
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3362, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.7776.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 186247962
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3363, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.7776.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 186247963
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3364, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.7776.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 186247964
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3365, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.7776.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 186247965
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3366, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.7776.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 186247966
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3367, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.7776.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 186247967
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3368, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.7776.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 186247968
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3369, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '31104.fx.7776.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 186247970
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 15552, 'characteristic': False, 'core_order': 3, 'counter': 3370, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '31104.fx.10368.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '10368.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '10368.pi', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3862291860621009286, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 10368, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '(C_2^3\\times C_6).S_3^3', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
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id: 186247971
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 7776, 'characteristic': False, 'core_order': 1, 'counter': 3371, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.10368.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10368.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10368, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
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id: 186247972
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1728, 'characteristic': False, 'core_order': 1, 'counter': 3372, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.10368.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10368.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10368, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
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id: 186247973
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': False, 'core_order': 1, 'counter': 3373, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.10368.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10368.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10368, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
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id: 186247974
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 3374, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.10368.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10368.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10368, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
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id: 186247975
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 3375, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.10368.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10368.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10368, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
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id: 186247976
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 3376, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.10368.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10368.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10368, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
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id: 186247977
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 3377, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.10368.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10368.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10368, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
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id: 186247978
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 3378, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.10368.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10368.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10368, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
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id: 186247979
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 5184, 'characteristic': False, 'core_order': 1, 'counter': 3379, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.15552.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '15552.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 15552, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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id: 186247981
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3456, 'characteristic': False, 'core_order': 1, 'counter': 3380, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.15552.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '15552.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 15552, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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id: 186247982
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1152, 'characteristic': False, 'core_order': 1, 'counter': 3381, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.15552.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '15552.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 15552, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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id: 186247983
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': False, 'core_order': 1, 'counter': 3382, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.15552.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '15552.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 15552, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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id: 186247984
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 3383, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.15552.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '15552.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 15552, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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id: 186247985
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 3384, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.15552.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '15552.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 15552, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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id: 186247986
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 3385, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.15552.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '15552.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 15552, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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id: 186247987
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 3386, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.15552.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '15552.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 15552, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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id: 186247988
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3387, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '31104.fx.15552.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '15552.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 15552, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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id: 186247989
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '31104.fx', 'ambient_counter': 154, 'ambient_order': 31104, 'ambient_tex': '(C_2^2\\times C_6^2).S_3^3', 'central': True, 'central_factor': False, 'centralizer_order': 31104, 'characteristic': True, 'core_order': 1, 'counter': 3388, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '31104.fx.31104.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '31104.a1', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '31104.fx', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4394578261467941646, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 31104, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '(C_2^2\\times C_6^2).S_3^3', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'PC', 'U0', 'D3', 'C9', 'Z', 'PC', 'U0', 'D3', 'C9'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
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gps_subgroup_data • Show schema
Hide schema
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id: 186245335
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': ['31104.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '2.b1', '2.c1', '2.d1', '2.e1', '3.a1', '3.b1', '16.d1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 6, 15552, 76, 22752, 12096, 18576, 36, 18144, 5712, 16056, 10368], 'label': '31104.fx.1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1', '2.b1', '2.c1', '2.d1', '2.e1'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1', 'subgroup_fusion': None, 'weyl_group': '31104.fx'}
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id: 186245336
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '4.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': ['7776.z1', '7776.bf1', '7776.be1', '7776.y1', '7776.bb1', '7776.bd1', '7776.ba1'], 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '2.c1', '2.d1'], 'contains': ['8.a1', '12.b1', '12.c1', '12.l1', '12.m1', '64.b1'], 'core': '4.b1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [12138, 2592, 5712, 10368, 15552, 76, 22752, 15984, 15624, 12096], 'label': '31104.fx.4.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': ['2.a1', '2.c1', '2.d1'], 'normal_contains': ['8.a1', '12.b1', '12.c1'], 'normalizer': '1.a1', 'old_label': '4.b1', 'projective_image': '31104.fx', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.b1', 'subgroup_fusion': None, 'weyl_group': '10368.pi'}
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id: 186245337
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '18.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.n1', '9.d1'], 'contains': ['36.r1', '36.s1', '36.x1', '36.cj1', '36.cz1', '54.by1', '54.ce1'], 'core': '72.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [5713, 10368, 2592, 18576, 6, 72, 22752, 12096, 15552], 'label': '31104.fx.18.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '18.bm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bm1', 'subgroup_fusion': None, 'weyl_group': '1728.39001'}
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id: 186245338
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.el1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bj1', '72.bk1', '72.bl1', '72.bp1', '108.cr1'], 'contains': ['432.bj1', '432.bo1', '432.bs1', '432.cq1', '432.fc1', '432.ff1', '432.gs1', '648.ec1', '648.ed1', '648.ee1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1, 10368, 22752, 36, 3096, 15552], 'label': '31104.fx.216.el1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cr1', 'old_label': '216.el1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.el1', 'subgroup_fusion': None, 'weyl_group': '72.49'}
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id: 186245339
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.em1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.bm1', '72.bp1', '108.cs1'], 'contains': ['432.bk1', '432.bn1', '432.ca1', '432.cn1', '432.fb1', '432.fg1', '432.gk1', '648.ec1', '648.ef1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1, 10368, 1728, 36, 3096, 15552], 'label': '31104.fx.216.em1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cs1', 'old_label': '216.em1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.em1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245340
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.en1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bn1', '72.bp1', '108.cu1'], 'contains': ['432.bl1', '432.bp1', '432.cb1', '432.co1', '432.fd1', '432.fo1', '432.gl1', '648.ed1', '648.ef1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [20737, 12384, 1728, 36, 3096, 15552], 'label': '31104.fx.216.en1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cu1', 'old_label': '216.en1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.en1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245341
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.eo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bo1', '72.bp1', '108.ct1'], 'contains': ['432.bm1', '432.bq1', '432.cc1', '432.cp1', '432.fe1', '432.fp1', '432.gm1', '648.ee1', '648.ef1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [20737, 12384, 1728, 36, 18216, 18144], 'label': '31104.fx.216.eo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ct1', 'old_label': '216.eo1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.eo1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245342
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ep1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bq1', '72.br1', '108.cr1'], 'contains': ['432.br1', '432.bt1', '432.ck1', '432.cu1', '432.ff1', '432.gh1', '432.gs1', '648.eg1', '648.eh1', '648.ei1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1, 10368, 22752, 2628, 3096, 15552], 'label': '31104.fx.216.ep1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cr1', 'old_label': '216.ep1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ep1', 'subgroup_fusion': None, 'weyl_group': '72.49'}
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id: 186245343
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.eq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.bq1', '108.cl1'], 'contains': ['432.fi1', '432.gd1', '432.go1', '648.eg1', '648.ej1', '864.ii1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1, 18144, 72, 15588, 12940, 10368], 'label': '31104.fx.216.eq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cl1', 'old_label': '216.eq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.eq1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186245344
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.er1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bq1', '108.cm1'], 'contains': ['432.fs1', '432.ge1', '432.gv1', '648.eh1', '648.ej1', '864.ij1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [20737, 18144, 72, 15588, 10924, 2016], 'label': '31104.fx.216.er1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cm1', 'old_label': '216.er1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.er1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186245345
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.es1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bq1', '72.bs1', '108.cn1'], 'contains': ['432.ft1', '432.gf1', '432.gw1', '648.ei1', '648.ej1', '864.ik1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [20737, 18144, 72, 15588, 556, 12384], 'label': '31104.fx.216.es1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cn1', 'old_label': '216.es1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.es1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186245346
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.et1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.br1', '108.cs1'], 'contains': ['432.bx1', '432.cd1', '432.cj1', '432.cr1', '432.fg1', '432.gg1', '432.gk1', '648.eg1', '648.ek1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1, 10368, 1728, 2628, 3096, 15552], 'label': '31104.fx.216.et1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cs1', 'old_label': '216.et1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.et1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245347
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.eu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.br1', '108.cu1'], 'contains': ['432.by1', '432.ce1', '432.cl1', '432.cs1', '432.fo1', '432.gi1', '432.gl1', '648.eh1', '648.ek1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [20737, 12384, 1728, 2628, 3096, 15552], 'label': '31104.fx.216.eu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cu1', 'old_label': '216.eu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.eu1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245348
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '24.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': ['1296.lr1'], 'conjugacy_class_count': 2, 'contained_in': ['8.a1', '12.a1', '12.b1', '12.d1', '12.l1', '12.n1', '12.r1', '12.w1'], 'contains': ['72.a1', '72.b1', '72.cr1', '72.cs1', '72.cz1', '96.i1', '96.n1'], 'core': '24.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [5712, 15624, 432, 12096, 10368, 15552, 2592, 22752], 'label': '31104.fx.24.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': ['8.a1', '12.a1', '12.b1', '12.d1'], 'normal_contains': ['72.a1', '72.b1'], 'normalizer': '1.a1', 'old_label': '24.a1', 'projective_image': '31104.fx', 'quotient_action_image': '24.14', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '24.a1', 'subgroup_fusion': None, 'weyl_group': '3456.di'}
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id: 186245349
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ev1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.br1', '72.bs1', '108.ct1'], 'contains': ['432.bz1', '432.cf1', '432.cm1', '432.ct1', '432.fp1', '432.gj1', '432.gm1', '648.ei1', '648.ek1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [20737, 12384, 1728, 15588, 18216, 18144], 'label': '31104.fx.216.ev1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ct1', 'old_label': '216.ev1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ev1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245350
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ew1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.bt1', '108.cl1', '108.co1', '108.do1'], 'contains': ['432.es1', '432.gd1', '432.hl1', '648.el1', '648.em1', '864.h1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [36, 10368, 18144, 3024, 12940, 18216], 'label': '31104.fx.216.ew1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.u1', 'old_label': '216.ew1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ew1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186245351
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ex1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bt1', '108.cm1', '108.cp1', '108.dr1'], 'contains': ['432.ex1', '432.ge1', '432.hr1', '648.el1', '648.eo1', '864.i1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [36, 2016, 18144, 3024, 10924, 18216], 'label': '31104.fx.216.ex1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '216.ex1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ex1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186245352
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ey1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bt1', '72.bu1', '72.bv1', '108.cn1', '108.cq1', '108.ds1'], 'contains': ['432.ey1', '432.gf1', '432.hs1', '648.el1', '648.en1', '864.j1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [36, 12384, 18144, 3024, 556, 18216], 'label': '31104.fx.216.ey1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.y1', 'old_label': '216.ey1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ey1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186245353
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ez1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.bw1', '108.cs1', '108.cv1', '108.du1'], 'contains': ['432.a1', '432.b1', '432.s1', '432.t1', '432.cv1', '432.cw1', '432.dl1', '432.dm1', '432.fb1', '432.gg1', '432.hk1', '648.em1', '648.ep1', '648.eq1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [36, 10368, 12096, 16056, 18144, 15552], 'label': '31104.fx.216.ez1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.be1', 'old_label': '216.ez1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ez1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 186245354
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.fa1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bt1', '72.bw1', '108.cr1', '108.cw1', '108.dv1'], 'contains': ['432.c1', '432.u1', '432.cx1', '432.dn1', '432.fc1', '432.gh1', '432.hn1', '648.em1', '648.en1', '648.eo1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [36, 10368, 22752, 16056, 3096, 15552], 'label': '31104.fx.216.fa1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '216.fa1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fa1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
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id: 186245355
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.fb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bu1', '72.bw1', '108.ct1', '108.cx1', '108.dw1'], 'contains': ['432.f1', '432.x1', '432.cy1', '432.do1', '432.fe1', '432.gj1', '432.ho1', '648.en1', '648.ep1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [36, 12384, 12096, 504, 18216, 18144], 'label': '31104.fx.216.fb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.r1', 'old_label': '216.fb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fb1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
-
id: 186245356
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.fc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bv1', '72.bw1', '108.dw1'], 'contains': ['432.g1', '432.y1', '432.cz1', '432.dp1', '432.fe1', '432.gj2', '432.hp1', '648.en1', '648.eq1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [36, 12384, 12096, 16056, 18216, 18144], 'label': '31104.fx.216.fc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bp1', 'old_label': '216.fc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fc1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
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id: 186245357
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.fd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bw1', '108.cu1', '108.cy1', '108.dw1'], 'contains': ['432.d1', '432.e1', '432.v1', '432.w1', '432.cy1', '432.cz1', '432.do2', '432.dp2', '432.fd1', '432.gi1', '432.hq1', '648.eo1', '648.ep1', '648.eq1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [36, 12384, 12096, 15552, 504, 18144], 'label': '31104.fx.216.fd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '216.fd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fd1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186245358
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.fe1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bx1', '72.by1', '72.bz1', '108.cr1', '108.cz1', '108.ex1'], 'contains': ['432.h1', '432.di1', '432.ed1', '432.ff1', '432.hn1', '648.er1', '648.es1', '648.et1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [10405, 15552, 10368, 16056, 2592, 22752], 'label': '31104.fx.216.fe1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bd1', 'old_label': '216.fe1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fe1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
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id: 186245359
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': ['1296.ls1', '1296.lu1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '12.c1', '12.e1', '12.j1', '12.o1', '12.t1'], 'contains': ['72.b1', '72.ct1', '72.cu1', '72.cx1', '72.dc1', '72.de1', '96.l1'], 'core': '24.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [76, 16056, 18576, 5712, 10368, 15552, 18144, 22752], 'label': '31104.fx.24.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': ['8.a1', '12.c1', '12.e1'], 'normal_contains': ['72.b1'], 'normalizer': '1.a1', 'old_label': '24.b1', 'projective_image': '31104.fx', 'quotient_action_image': '24.14', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '24.b1', 'subgroup_fusion': None, 'weyl_group': '3456.di'}
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id: 186245360
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ff1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.bx1', '108.cs1', '108.dd1', '108.ey1'], 'contains': ['432.i1', '432.dj1', '432.dz1', '432.fg1', '432.hk1', '648.er1', '648.eu1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [10405, 1728, 15552, 16056, 2592, 10368], 'label': '31104.fx.216.ff1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '216.ff1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ff1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245361
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.fg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.by1', '108.cl1', '108.da1', '108.ez1'], 'contains': ['432.fi1', '432.hl1', '648.er1', '648.ev1', '864.r1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [10405, 18144, 72, 2664, 10368, 12940], 'label': '31104.fx.216.fg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '216.fg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fg1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
-
id: 186245362
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.fh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.bz1', '108.fc1'], 'contains': ['432.fm1', '432.hm1', '648.er1', '648.ew1', '864.s1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [10405, 15552, 3096, 18144, 10368, 29404], 'label': '31104.fx.216.fh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cp1', 'old_label': '216.fh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fh1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
-
id: 186245363
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.fi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bx1', '72.ca1', '108.ct1', '108.de1', '108.fe1'], 'contains': ['432.k1', '432.dk1', '432.ei1', '432.fp1', '432.ho1', '648.es1', '648.eu1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [10405, 1728, 18144, 2664, 15552, 12384], 'label': '31104.fx.216.fi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '216.fi1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fi1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 186245364
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.fj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bx1', '108.cu1', '108.df1', '108.fe1'], 'contains': ['432.j1', '432.dk1', '432.eh1', '432.fo1', '432.hq1', '648.et1', '648.eu1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [10405, 1728, 15552, 16056, 18144, 12384], 'label': '31104.fx.216.fj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '216.fj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fj1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245365
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.fk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.by1', '108.cm1', '108.db1', '108.ff1'], 'contains': ['432.fs1', '432.hr1', '648.et1', '648.ev1', '864.v1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [10405, 18144, 72, 2664, 2016, 12940], 'label': '31104.fx.216.fk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '216.fk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fk1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
-
id: 186245366
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.fl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.by1', '72.ca1', '108.cn1', '108.dc1', '108.fg1'], 'contains': ['432.ft1', '432.hs1', '648.es1', '648.ev1', '864.w1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [10405, 18144, 72, 2664, 12384, 12940], 'label': '31104.fx.216.fl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '216.fl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fl1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
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id: 186246923
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.ht1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.bs1', '288.du1', '432.oi1'], 'contains': ['1728.bk1', '1728.dn1', '2592.fr1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [1, 12138, 8212, 5712], 'label': '31104.fx.864.ht1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.oi1', 'old_label': '864.ht1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ht1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 186245367
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.fm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bz1', '72.ca1', '108.fi1'], 'contains': ['432.fz1', '432.hu1', '648.es1', '648.ew1', '864.x1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [10405, 15552, 3096, 16056, 2016, 29404], 'label': '31104.fx.216.fm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cp1', 'old_label': '216.fm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fm1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
-
id: 186245368
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.fn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bz1', '108.fi2'], 'contains': ['432.fy1', '432.hw1', '648.et1', '648.ew1', '864.y1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [10405, 15552, 3096, 16056, 12384, 29404], 'label': '31104.fx.216.fn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cp1', 'old_label': '216.fn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fn1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
-
id: 186245369
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.fo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.cb1', '108.da1', '108.dg1', '108.do1'], 'contains': ['432.gd1', '432.hl1', '648.ex1', '648.ey1', '864.z1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [15588, 10368, 18144, 3024, 12940, 18216], 'label': '31104.fx.216.fo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.u1', 'old_label': '216.fo1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fo1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
-
id: 186245370
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1', '8.b1'], 'contains': ['48.e1', '48.n1', '48.t1', '72.bg1', '72.bh1', '72.bi1', '72.bj1', '72.bk1', '72.bl1', '96.p1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [1, 12384, 10368, 36, 5712, 15552, 18648, 76], 'label': '31104.fx.24.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1', 'old_label': '24.c1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1', 'subgroup_fusion': None, 'weyl_group': '1296.3551'}
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id: 186245371
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.fp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cb1', '108.db1', '108.dh1', '108.dr1'], 'contains': ['432.ge1', '432.hr1', '648.ex1', '648.fa1', '864.ba1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [15588, 2016, 18144, 3024, 10924, 18216], 'label': '31104.fx.216.fp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '216.fp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fp1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186245372
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.fq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cb1', '72.cc1', '72.cd1', '108.dc1', '108.di1', '108.ds1'], 'contains': ['432.gf1', '432.hs1', '648.ex1', '648.ez1', '864.bb1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [15588, 12384, 18144, 3024, 556, 18216], 'label': '31104.fx.216.fq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.y1', 'old_label': '216.fq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fq1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
-
id: 186245373
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.fr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ce1', '108.dd1', '108.dj1', '108.du1'], 'contains': ['432.l1', '432.l2', '432.m1', '432.dl1', '432.dm1', '432.dq1', '432.dr1', '432.gg1', '432.hk1', '648.ey1', '648.fb1', '648.fc1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [468, 10368, 12096, 16056, 18144, 15552], 'label': '31104.fx.216.fr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.be1', 'old_label': '216.fr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fr1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186245374
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.fs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cb1', '72.ce1', '108.cz1', '108.dm1', '108.dv1'], 'contains': ['432.n1', '432.dn1', '432.ds1', '432.gh1', '432.hn1', '648.ey1', '648.ez1', '648.fa1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [18612, 10368, 22752, 18144, 3096, 15552], 'label': '31104.fx.216.fs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '216.fs1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fs1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
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id: 186245375
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ft1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cc1', '72.ce1', '108.de1', '108.dk1', '108.dw1'], 'contains': ['432.q1', '432.do2', '432.dt1', '432.gj2', '432.ho1', '648.ez1', '648.fb1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [15588, 12384, 12096, 504, 18216, 18144], 'label': '31104.fx.216.ft1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.r1', 'old_label': '216.ft1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ft1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
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id: 186245376
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.fu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cd1', '72.ce1', '108.dw1'], 'contains': ['432.r1', '432.r2', '432.dp2', '432.du1', '432.gj1', '432.gj2', '432.hp1', '648.ez1', '648.fc1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [18612, 12384, 12096, 16056, 18216, 18144], 'label': '31104.fx.216.fu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bp1', 'old_label': '216.fu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fu1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
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id: 186245377
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.fv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ce1', '108.df1', '108.dl1', '108.dw1'], 'contains': ['432.o1', '432.p1', '432.do1', '432.dp1', '432.dt1', '432.du1', '432.gi1', '432.hq1', '648.fa1', '648.fb1', '648.fc1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [18252, 12384, 12096, 15552, 504, 18144], 'label': '31104.fx.216.fv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '216.fv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fv1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186245378
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.fw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.cf1', '108.cs1', '108.dj1', '108.fl1'], 'contains': ['432.z1', '432.dv1', '432.eb1', '432.gk1', '432.hk1', '648.fd1', '648.fe1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1, 10368, 15552, 16056, 2592, 1728], 'label': '31104.fx.216.fw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.be1', 'old_label': '216.fw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fw1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245379
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.fx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cf1', '72.cg1', '72.ch1', '108.ct1', '108.dk1', '108.fm1'], 'contains': ['432.bb1', '432.dw1', '432.ek2', '432.gm1', '432.ho1', '648.fd1', '648.ff1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1, 12384, 18144, 2664, 15552, 1728], 'label': '31104.fx.216.fx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '216.fx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fx1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245380
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.fy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cf1', '108.cu1', '108.dl1', '108.fm1'], 'contains': ['432.ba1', '432.dw1', '432.ek1', '432.gl1', '432.hq1', '648.fd1', '648.fg1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1, 12384, 15552, 16056, 18144, 1728], 'label': '31104.fx.216.fy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '216.fy1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fy1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 186245381
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1', '8.b1'], 'contains': ['48.a1', '48.b1', '48.c1', '48.d1', '48.f1', '48.i1', '48.q1', '72.bj1', '72.bn1', '72.bp1'], 'core': '576.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [1, 10924, 12096, 36, 15552, 12384, 4032, 3096], 'label': '31104.fx.24.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.d1', 'old_label': '24.d1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1', 'subgroup_fusion': None, 'weyl_group': '648.610'}
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id: 186245382
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.fz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ci1', '108.cl1', '108.dg1', '108.fn1'], 'contains': ['432.go1', '432.hl1', '648.fe1', '648.fh1', '648.fi1', '864.bu1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1, 18144, 72, 2664, 10924, 10368], 'label': '31104.fx.216.fz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.u1', 'old_label': '216.fz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fz1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
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id: 186245383
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ga1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cf1', '72.ci1', '108.cr1', '108.dm1', '108.fr1'], 'contains': ['432.bc1', '432.dx1', '432.ef1', '432.gs1', '432.hn1', '648.fe1', '648.ff1', '648.fg1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1, 10368, 22752, 16056, 2592, 15552], 'label': '31104.fx.216.ga1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '216.ga1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ga1', 'subgroup_fusion': None, 'weyl_group': '144.196'}
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id: 186245384
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.gb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ci1', '108.cm1', '108.dh1', '108.fs1'], 'contains': ['432.gv1', '432.hr1', '648.fg1', '648.fh1', '648.fi1', '864.bw1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1, 18144, 72, 2664, 10924, 2016], 'label': '31104.fx.216.gb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '216.gb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gb1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
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id: 186245385
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.gc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cg1', '72.ci1', '108.cn1', '108.di1', '108.ft1'], 'contains': ['432.gw1', '432.hs1', '648.ff1', '648.fh1', '864.bx1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1, 18144, 72, 2664, 556, 12384], 'label': '31104.fx.216.gc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.r1', 'old_label': '216.gc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gc1', 'subgroup_fusion': None, 'weyl_group': '864.4000'}
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id: 186245386
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.gd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ch1', '72.ci1', '108.fv1'], 'contains': ['432.ha1', '432.ht1', '648.ff1', '648.fi1', '864.by1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1, 18144, 72, 2664, 10924, 12384], 'label': '31104.fx.216.gd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.db1', 'old_label': '216.gd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gd1', 'subgroup_fusion': None, 'weyl_group': '432.535'}
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id: 186245387
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ge1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.cj1', '108.cv1', '108.dj1', '108.ey1'], 'contains': ['432.dy1', '432.dz1', '432.hk1', '648.fj1', '648.fp1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [10837, 1728, 2592, 16056, 22752, 15552], 'label': '31104.fx.216.ge1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '216.ge1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ge1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 186245388
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.gf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ck1', '108.cv1', '108.dd1', '108.fl1'], 'contains': ['432.ea1', '432.eb1', '432.hk1', '648.fk1', '648.fq1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [433, 10368, 2592, 16056, 1728, 15552], 'label': '31104.fx.216.gf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.be1', 'old_label': '216.gf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gf1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 186245389
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.gg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.cl1', '108.co1', '108.dg1', '108.ez1'], 'contains': ['432.hl1', '648.fj1', '648.fr1', '864.cb1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [28981, 18144, 18216, 22752, 2592, 31084], 'label': '31104.fx.216.gg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '216.gg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gg1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
-
id: 186245390
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.gh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.cm1', '108.co1', '108.da1', '108.fn1'], 'contains': ['432.hl1', '648.fk1', '648.fs1', '648.ft1', '864.cc1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [18577, 18144, 18216, 2592, 29068, 10368], 'label': '31104.fx.216.gh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.u1', 'old_label': '216.gh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gh1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
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id: 186245391
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.gi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.cn1', '108.fc1'], 'contains': ['432.hm1', '648.fj1', '648.fu1', '864.cd1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [28981, 15552, 18648, 10368, 2592, 27316], 'label': '31104.fx.216.gi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cp1', 'old_label': '216.gi1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gi1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186245392
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1', '12.f1'], 'contains': ['48.g1', '48.j1', '48.r1', '72.bk1', '72.bo1', '72.bp1', '96.s1'], 'core': '576.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [1, 4032, 12384, 36, 12096, 18144, 72, 10924], 'label': '31104.fx.24.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1', 'old_label': '24.e1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1', 'subgroup_fusion': None, 'weyl_group': '1296.2940'}
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id: 186245393
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.gj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cj1', '72.cl1', '72.cn1', '108.cw1', '108.dm1', '108.ex1'], 'contains': ['432.ec1', '432.ed1', '432.hn1', '648.fj1', '648.fl1', '648.fm1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [10837, 2592, 15552, 16056, 22752, 10368], 'label': '31104.fx.216.gj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bd1', 'old_label': '216.gj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gj1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
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id: 186245394
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.gk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ck1', '72.cm1', '108.cw1', '108.cz1', '108.fr1'], 'contains': ['432.ee1', '432.ef1', '432.hn1', '648.fk1', '648.fn1', '648.fo1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [433, 10368, 22752, 16056, 15552, 2592], 'label': '31104.fx.216.gk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '216.gk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gk1', 'subgroup_fusion': None, 'weyl_group': '144.196'}
-
id: 186245395
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.gl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cj1', '72.co1', '108.cx1', '108.dk1', '108.fe1'], 'contains': ['432.eg1', '432.eh1', '432.ho1', '648.fl1', '648.fp1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [28981, 1728, 15552, 2664, 12384, 2592], 'label': '31104.fx.216.gl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '216.gl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gl1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245396
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.gm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cj1', '108.cy1', '108.dl1', '108.fe1'], 'contains': ['432.eg1', '432.ei1', '432.hq1', '648.fm1', '648.fp1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [28981, 1728, 15552, 16056, 12384, 2592], 'label': '31104.fx.216.gm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '216.gm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gm1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245397
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.gn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ck1', '72.cp1', '72.cq1', '108.cx1', '108.de1', '108.fm1'], 'contains': ['432.ej1', '432.ek1', '432.ho1', '648.fn1', '648.fq1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [18577, 12384, 15552, 2664, 1728, 2592], 'label': '31104.fx.216.gn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '216.gn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gn1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245398
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.go1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ck1', '108.cy1', '108.df1', '108.fm1'], 'contains': ['432.ej1', '432.ek2', '432.hq1', '648.fo1', '648.fq1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [18577, 12384, 15552, 16056, 1728, 2592], 'label': '31104.fx.216.go1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '216.go1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.go1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245399
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.gp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cl1', '108.cp1', '108.dh1', '108.ff1'], 'contains': ['432.hr1', '648.fm1', '648.fr1', '864.ck1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [28981, 18144, 18216, 2016, 2592, 31084], 'label': '31104.fx.216.gp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '216.gp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gp1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
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id: 186245400
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.gq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cm1', '108.cp1', '108.db1', '108.fs1'], 'contains': ['432.hr1', '648.fo1', '648.fs1', '648.ft1', '864.cl1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [18577, 18144, 18216, 2592, 29068, 2016], 'label': '31104.fx.216.gq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '216.gq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gq1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
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id: 186245401
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.gr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cl1', '72.co1', '108.cq1', '108.di1', '108.fg1'], 'contains': ['432.hs1', '648.fl1', '648.fr1', '864.cm1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [28981, 18144, 18216, 12384, 2592, 31084], 'label': '31104.fx.216.gr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '216.gr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gr1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
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id: 186245402
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.gs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cm1', '72.cp1', '108.cq1', '108.dc1', '108.ft1'], 'contains': ['432.hs1', '648.fn1', '648.fs1', '864.cn1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [18577, 18144, 18216, 2592, 18700, 12384], 'label': '31104.fx.216.gs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.r1', 'old_label': '216.gs1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gs1', 'subgroup_fusion': None, 'weyl_group': '864.4000'}
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id: 186245403
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.g1', '8.b1'], 'contains': ['48.h1', '48.k1', '48.s1', '72.bl1', '72.bm1', '72.bp1', '96.t1'], 'core': '576.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [1, 22752, 10368, 36, 12096, 15552, 18648, 5712], 'label': '31104.fx.24.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '24.f1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1', 'subgroup_fusion': None, 'weyl_group': '1296.2940'}
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id: 186245404
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.gt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cm1', '72.cq1', '108.fv1'], 'contains': ['432.ht1', '648.fn1', '648.ft1', '864.co1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [18577, 18144, 18216, 2592, 29068, 12384], 'label': '31104.fx.216.gt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.db1', 'old_label': '216.gt1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gt1', 'subgroup_fusion': None, 'weyl_group': '432.535'}
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id: 186245405
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.gu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cn1', '72.co1', '108.fi1'], 'contains': ['432.hu1', '648.fl1', '648.fu1', '864.cp1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [28981, 15552, 18648, 2016, 2592, 27316], 'label': '31104.fx.216.gu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cp1', 'old_label': '216.gu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gu1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
-
id: 186245406
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.gv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cn1', '108.fi2'], 'contains': ['432.hw1', '648.fm1', '648.fu1', '864.cq1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [28981, 15552, 18648, 12384, 2592, 27316], 'label': '31104.fx.216.gv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cp1', 'old_label': '216.gv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gv1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186245407
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.gw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.a1', '72.cr1', '72.cs1', '108.du1', '108.dx1', '108.ea1', '108.ei1', '108.eu1', '108.ey1', '108.fl1'], 'contains': ['432.el1', '432.em1', '432.hk1', '648.a1', '648.fw1'], 'core': '648.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [16056, 10368, 12096, 18576, 18144, 15552], 'label': '31104.fx.216.gw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '216.gw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gw1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186245408
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.gx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.df1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ct1', '72.cu1', '72.cx1', '108.do1', '108.ez1', '108.fn1'], 'contains': ['432.hl1', '648.a1', '648.fx1', '648.fz1', '864.cx1'], 'core': '648.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [18576, 18144, 72, 15552, 10924, 10368], 'label': '31104.fx.216.gx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '216.gx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gx1', 'subgroup_fusion': None, 'weyl_group': '144.189'}
-
id: 186245409
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.gy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.b1', '72.ct1', '72.cu1', '108.dp1', '108.eb1', '108.ec1', '108.eh1', '108.ev1', '108.fa1', '108.fo1'], 'contains': ['648.a1', '648.fy1', '648.ga1', '864.cz1', '864.ge1'], 'core': '648.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [76, 15552, 2592, 10368, 2664, 18576], 'label': '31104.fx.216.gy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '216.gy1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gy1', 'subgroup_fusion': None, 'weyl_group': '1152.157852'}
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id: 186245410
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.gz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.b1', '72.cs1', '72.ct1', '72.cw1', '108.el1', '108.em1', '108.fq1'], 'contains': ['648.a1', '648.ga1', '864.db1', '864.gg1'], 'core': '648.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [28464, 15552, 2592, 10368, 15624, 432], 'label': '31104.fx.216.gz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '216.gz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gz1', 'subgroup_fusion': None, 'weyl_group': '1728.47855'}
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id: 186245411
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ha1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.df1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.cv1', '72.cw1', '72.cy1', '108.fc1'], 'contains': ['432.hm1', '648.a1', '648.gb1', '864.dc1'], 'core': '648.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [18576, 15552, 18648, 18144, 22132, 10368], 'label': '31104.fx.216.ha1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.u1', 'old_label': '216.ha1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ha1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
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id: 186245412
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.hb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.cr1', '72.cs1', '72.cz1', '108.dz1', '108.en1', '108.fd1'], 'contains': ['648.a1', '648.gc1', '864.de1', '864.gh1', '864.gh2'], 'core': '648.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [29904, 15552, 2592, 10368, 15624, 432], 'label': '31104.fx.216.hb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1', 'old_label': '216.hb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hb1', 'subgroup_fusion': None, 'weyl_group': '576.5512'}
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id: 186245413
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.hb2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.cv1', '72.cw1', '72.cz1', '108.ed1', '108.ew1', '108.fd2'], 'contains': ['648.a1', '648.gc1', '864.de2', '864.gh3'], 'core': '648.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [24268, 15552, 2592, 10368, 2664, 18576], 'label': '31104.fx.216.hb2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1', 'old_label': '216.hb2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hb2', 'subgroup_fusion': None, 'weyl_group': '576.8654'}
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id: 186245414
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1'], 'contains': ['48.j1', '48.p1', '48.r1', '72.bq1', '72.br1', '72.bs1', '96.bc1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [1, 4032, 12384, 15588, 12096, 18144, 72, 10924], 'label': '31104.fx.24.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1', 'old_label': '24.g1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.g1', 'subgroup_fusion': None, 'weyl_group': '1296.2940'}
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id: 186245415
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.hc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1', '72.da1', '72.db1', '108.dw1', '108.fe1', '108.fm1'], 'contains': ['432.eo1', '432.ep1', '432.ho1', '432.hp1', '432.hq1', '648.fv1', '648.fw1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [16056, 12384, 12096, 18576, 18144, 15552], 'label': '31104.fx.216.hc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '216.hc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hc1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186245416
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.hd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.df1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cx1', '72.dc1', '72.de1', '108.dr1', '108.ff1', '108.fs1'], 'contains': ['432.hr1', '648.fv1', '648.fx1', '648.fz1', '864.di1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [18576, 18144, 72, 15552, 10924, 2016], 'label': '31104.fx.216.hd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '216.hd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hd1', 'subgroup_fusion': None, 'weyl_group': '144.189'}
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id: 186245417
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.he1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.df1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cx1', '72.da1', '72.dd1', '72.de1', '108.ds1', '108.fg1', '108.ft1'], 'contains': ['432.hs1', '648.fv1', '648.fx1', '864.dj1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [18576, 18144, 72, 15552, 556, 12384], 'label': '31104.fx.216.he1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '216.he1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.he1', 'subgroup_fusion': None, 'weyl_group': '432.747'}
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id: 186245418
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.hf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.b1', '72.dc1', '72.de1', '108.dt1', '108.fh1', '108.fu1'], 'contains': ['648.fv1', '648.fy1', '648.ga1', '864.dm1', '864.dn1', '864.gk1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [5712, 15552, 2592, 12384, 15624, 432], 'label': '31104.fx.216.hf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '216.hf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hf1', 'subgroup_fusion': None, 'weyl_group': '576.8657'}
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id: 186245419
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.hg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.df1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cx1', '72.db1', '72.dc1', '72.df1', '108.fv1'], 'contains': ['432.ht1', '648.fv1', '648.fz1', '864.do1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [18576, 18144, 72, 15552, 10924, 12384], 'label': '31104.fx.216.hg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.e1', 'old_label': '216.hg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hg1', 'subgroup_fusion': None, 'weyl_group': '216.164'}
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id: 186245420
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.hh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.df1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cy1', '72.da1', '72.db1', '108.fi1'], 'contains': ['432.hu1', '432.hv1', '648.fv1', '648.gb1', '864.dq1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [18576, 15552, 18648, 18144, 13780, 2016], 'label': '31104.fx.216.hh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.q1', 'old_label': '216.hh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hh1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
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id: 186245421
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.hh2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.df1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cy1', '72.dd1', '72.df1', '108.fi2'], 'contains': ['432.hw1', '648.fv1', '648.gb1', '864.dr1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [18576, 15552, 18648, 18144, 24148, 12384], 'label': '31104.fx.216.hh2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1', 'old_label': '216.hh2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hh2', 'subgroup_fusion': None, 'weyl_group': '72.43'}
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id: 186245422
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.hi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.cz1', '72.dd1', '72.df1', '108.fj1'], 'contains': ['648.fv1', '648.gc1', '864.du1', '864.dv1', '864.gl1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [364, 15552, 2592, 12384, 2664, 18576], 'label': '31104.fx.216.hi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1', 'old_label': '216.hi1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hi1', 'subgroup_fusion': None, 'weyl_group': '288.1026'}
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id: 186245423
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.hj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ct1', '72.cu1', '72.dc1', '72.de1', '108.fw1'], 'contains': ['648.fx1', '648.fy1', '648.fz1', '648.ga1', '864.dw1', '864.dy1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [22828, 15552, 18144, 5712, 16056, 18576], 'label': '31104.fx.216.hj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '216.hj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hj1', 'subgroup_fusion': None, 'weyl_group': '288.1026'}
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id: 186245424
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.hk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ct1', '72.dc1', '72.de1', '108.fx1'], 'contains': ['648.fx1', '648.fz1', '648.ga1', '864.dx1', '864.dz1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [2092, 15552, 18144, 28464, 16056, 18576], 'label': '31104.fx.216.hk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '216.hk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hk1', 'subgroup_fusion': None, 'weyl_group': '288.1026'}
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id: 186245425
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1', '12.g1', '12.k1'], 'contains': ['48.g1', '48.p1', '48.u1', '72.bt1', '72.bu1', '72.bv1', '72.bw1', '96.a1'], 'core': '576.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [36, 18144, 12096, 16056, 72, 12384, 4032, 10924], 'label': '31104.fx.24.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.h1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.h1', 'subgroup_fusion': None, 'weyl_group': '1296.2940'}
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id: 186245634
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.df1', '96.j1'], 'contains': ['864.do1', '864.ds1', '864.du1', '1152.q1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [364, 15552, 29904, 12384, 18648], 'label': '31104.fx.288.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.j1', 'old_label': '288.bz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bz1', 'subgroup_fusion': None, 'weyl_group': '36.11'}
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id: 186245426
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.hl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cu1', '72.de1', '108.dn1', '108.ef1', '108.ep1', '108.fk1', '108.fy1'], 'contains': ['648.fx1', '648.fy1', '864.ea1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [20812, 15552, 18144, 5712, 16056, 18576], 'label': '31104.fx.216.hl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '216.hl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hl1', 'subgroup_fusion': None, 'weyl_group': '576.8654'}
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id: 186245427
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.hm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ct1', '72.de1', '108.eq1', '108.fz1'], 'contains': ['648.fx1', '648.ga1', '864.eb1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [76, 15552, 18144, 28464, 16056, 18576], 'label': '31104.fx.216.hm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.m1', 'old_label': '216.hm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hm1', 'subgroup_fusion': None, 'weyl_group': '576.8654'}
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id: 186245428
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.hn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ct1', '72.cu1', '72.dc1', '108.er1', '108.es1', '108.ga1'], 'contains': ['648.fy1', '648.fz1', '648.ga1', '864.ec1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [76, 15552, 18144, 5712, 16056, 18576], 'label': '31104.fx.216.hn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.m1', 'old_label': '216.hn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hn1', 'subgroup_fusion': None, 'weyl_group': '576.8654'}
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id: 186245429
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ho1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cu1', '72.dc1', '108.eg1', '108.gb1'], 'contains': ['648.fy1', '648.fz1', '864.ed1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [12460, 15552, 18144, 5712, 16056, 18576], 'label': '31104.fx.216.ho1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '216.ho1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ho1', 'subgroup_fusion': None, 'weyl_group': '576.8654'}
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id: 186245430
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.hp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ct1', '72.dc1', '108.et1', '108.gc2'], 'contains': ['648.fz1', '648.ga1', '864.ee1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [10444, 15552, 18144, 28464, 16056, 18576], 'label': '31104.fx.216.hp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.m1', 'old_label': '216.hp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hp1', 'subgroup_fusion': None, 'weyl_group': '576.8654'}
-
id: 186245431
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.hp2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ct1', '72.dc1', '108.gc1'], 'contains': ['648.fz1', '648.ga1', '864.ee2'], 'core': '1944.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [22828, 15552, 18144, 28464, 16056, 18576], 'label': '31104.fx.216.hp2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '216.hp2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hp2', 'subgroup_fusion': None, 'weyl_group': '288.1026'}
-
id: 186245432
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.hq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.dg1', '108.b1', '108.gf1', '108.gi1'], 'contains': ['432.hx1', '432.ic1', '432.if1', '432.io1', '432.ir1', '432.kj1', '432.km1', '648.gd1', '648.ge1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 10368, 12096, 2598, 36, 18576], 'label': '31104.fx.216.hq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.hq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hq1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186245433
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.hr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.dh1', '108.c1', '108.gf1', '108.gi1'], 'contains': ['432.hx1', '432.if1', '432.ih1', '432.is1', '432.it1', '432.kn1', '432.ko1', '648.gf1', '648.gg1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [8305, 10368, 12096, 2598, 36, 18576], 'label': '31104.fx.216.hr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.hr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hr1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186245434
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.hs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.dg1', '108.d1', '108.gg1', '108.gk1'], 'contains': ['432.ia1', '432.ib1', '432.ii1', '432.jb1', '432.jk1', '432.jt1', '432.kc1', '648.gd1', '648.gj1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 10368, 22752, 21606, 36, 18576], 'label': '31104.fx.216.hs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.hs1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hs1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186245435
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ht1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.dg1', '108.b1', '108.gh1', '108.gj1'], 'contains': ['432.hy1', '432.ic1', '432.ie1', '432.jc1', '432.jj1', '432.ju1', '432.kb1', '648.ge1', '648.gj1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 10368, 12096, 2670, 36, 18576], 'label': '31104.fx.216.ht1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.ht1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ht1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186245436
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '24.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1', '12.h1', '12.q1'], 'contains': ['48.j1', '48.u1', '72.bx1', '72.by1', '72.bz1', '72.ca1', '96.b1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [10405, 1728, 12384, 2664, 12940, 18144, 72, 10368], 'label': '31104.fx.24.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.i1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.i1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
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id: 186245437
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.hu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.dh1', '108.c1', '108.gh1', '108.gj1'], 'contains': ['432.hy1', '432.ie1', '432.ih1', '432.jl1', '432.jm1', '432.kd1', '432.ke1', '648.gg1', '648.gk1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [8305, 10368, 12096, 2670, 36, 18576], 'label': '31104.fx.216.hu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.hu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hu1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186245438
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.hv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.u1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.dh1', '108.e1', '108.gg1', '108.gk1'], 'contains': ['432.ia1', '432.ii1', '432.ij1', '432.jn1', '432.jo1', '432.kf1', '432.kg1', '648.gf1', '648.gk1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [8305, 10368, 22752, 21606, 36, 18576], 'label': '31104.fx.216.hv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.hv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hv1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186245439
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.hw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.di1', '108.b1', '108.gi1', '108.gj1'], 'contains': ['432.hx1', '432.hy1', '432.ic1', '432.il1', '432.iz1', '432.jp1', '432.kp1', '432.ol1', '432.on1', '648.gh1', '648.gl1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 10368, 12096, 6, 36, 18576], 'label': '31104.fx.216.hw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.hw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hw1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186245440
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.hx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.dj1', '108.c1', '108.gi1', '108.gj1'], 'contains': ['432.hx1', '432.hy1', '432.ih1', '432.im1', '432.ja1', '432.jq1', '432.kq1', '648.gi1', '648.gm1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [8305, 10368, 12096, 6, 36, 18576], 'label': '31104.fx.216.hx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.hx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hx1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186245441
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.hy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.di1', '108.d1', '108.gk1'], 'contains': ['432.ia1', '432.ib1', '432.iu1', '432.jr1', '432.kh1', '432.om1', '432.oo1', '648.gl1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [5713, 10368, 22752, 24198, 36, 18576], 'label': '31104.fx.216.hy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.hy1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hy1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186245442
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.hz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dj1', '108.e1', '108.gk1'], 'contains': ['432.ia1', '432.ij1', '432.iy1', '432.js1', '432.ki1', '648.gm1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [8305, 10368, 22752, 24198, 36, 18576], 'label': '31104.fx.216.hz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.hz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hz1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186245443
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ia1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dk1', '108.d1', '108.gg1'], 'contains': ['432.ib1', '432.ii1', '432.kt1', '432.lm1', '432.ln1', '648.gn1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [5713, 10368, 22752, 24270, 36, 18576], 'label': '31104.fx.216.ia1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.ia1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ia1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186245444
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ib1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.dk1', '108.b1', '108.gf1', '108.gh1'], 'contains': ['432.ic1', '432.ie1', '432.if1', '432.ky1', '432.kz1', '432.lk1', '432.ll1', '648.gn1', '648.go1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 10368, 12096, 78, 36, 18576], 'label': '31104.fx.216.ib1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.ib1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ib1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186246924
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.hu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.bt1', '288.du1'], 'contains': ['1728.bl1', '1728.dq1', '2592.fr1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [1, 22506, 8212, 16080], 'label': '31104.fx.864.hu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '864.hu1', 'old_label': '864.hu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.hu1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 186245445
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ic1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.dl1', '108.c1', '108.gf1', '108.gh1'], 'contains': ['432.ie1', '432.if1', '432.ih1', '432.lo1', '432.lp1', '432.lq1', '432.lr1', '648.gp1', '648.gq1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [8305, 10368, 12096, 78, 36, 18576], 'label': '31104.fx.216.ic1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.ic1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ic1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186245446
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.id1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dl1', '108.e1', '108.gg1'], 'contains': ['432.ii1', '432.ij1', '432.ls1', '432.lt1', '432.lu1', '648.gp1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [8305, 10368, 22752, 24270, 36, 18576], 'label': '31104.fx.216.id1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.id1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.id1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186245447
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '4.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': ['7776.y1', '7776.bb1', '7776.z1', '7776.be1', '7776.bf1', '7776.ba1', '7776.bc1'], 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '2.c1', '2.e1'], 'contains': ['8.a1', '12.d1', '12.n1', '12.o1', '12.p1', '64.c1'], 'core': '4.c1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [26047, 18144, 10368, 22752, 15552, 5712, 12096, 18576, 16056, 3100], 'label': '31104.fx.4.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': ['2.a1', '2.c1', '2.e1'], 'normal_contains': ['8.a1', '12.d1'], 'normalizer': '1.a1', 'old_label': '4.c1', 'projective_image': '31104.fx', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.c1', 'subgroup_fusion': None, 'weyl_group': '10368.pi'}
-
id: 186245448
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '24.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1', '12.i1', '12.k1'], 'contains': ['48.p1', '48.u1', '72.cb1', '72.cc1', '72.cd1', '72.ce1', '96.c1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [15588, 18144, 12096, 16056, 72, 12384, 4032, 10924], 'label': '31104.fx.24.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.j1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.j1', 'subgroup_fusion': None, 'weyl_group': '1296.2940'}
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id: 186245449
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ie1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.dm1', '108.b1', '108.gl1', '108.go1'], 'contains': ['432.il1', '432.ip1', '432.ir1', '432.jv1', '432.kb1', '432.ku1', '432.kz1', '648.gr1', '648.gt1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 10368, 12096, 2670, 108, 18576], 'label': '31104.fx.216.ie1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.ie1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ie1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186245450
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.if1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.dn1', '108.c1', '108.gl1', '108.go1'], 'contains': ['432.im1', '432.ip1', '432.is1', '432.jv1', '432.ke1', '432.la1', '432.lp1', '648.gs1', '648.gu1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [8305, 10368, 12096, 2670, 108, 18576], 'label': '31104.fx.216.if1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.if1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.if1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186245451
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ig1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.do1', '108.f1', '108.gi1', '108.gl1'], 'contains': ['432.il1', '432.in1', '432.is1', '432.jy1', '432.kj1', '432.kq1', '432.kw1', '648.gv1', '648.gx1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [8305, 10368, 12096, 6, 2628, 18576], 'label': '31104.fx.216.ig1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.ig1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ig1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186245452
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ih1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.dp1', '108.g1', '108.gi1', '108.gl1'], 'contains': ['432.im1', '432.in1', '432.ir1', '432.jy1', '432.kn1', '432.kp1', '432.ld1', '648.gw1', '648.gy1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 10368, 12096, 6, 2628, 18576], 'label': '31104.fx.216.ih1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.ih1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ih1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186245453
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ii1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.dq1', '108.f1', '108.gf1', '108.go1'], 'contains': ['432.io1', '432.iq1', '432.is1', '432.kw2', '432.kz1', '432.lh1', '432.lr1', '648.gz1', '648.ha1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [8305, 10368, 12096, 78, 2700, 18576], 'label': '31104.fx.216.ii1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.ii1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ii1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186245454
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ij1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.dr1', '108.g1', '108.gf1', '108.go1'], 'contains': ['432.iq1', '432.ir1', '432.it1', '432.ld2', '432.lh1', '432.ll1', '432.lp1', '648.hb1', '648.hc1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 10368, 12096, 78, 2700, 18576], 'label': '31104.fx.216.ij1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.ij1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ij1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186245455
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ik1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.dm1', '108.d1', '108.gm1', '108.gq1'], 'contains': ['432.iu1', '432.jf1', '432.jk1', '432.jx1', '432.kc1', '432.kr1', '432.kt1', '648.gr1', '648.hh1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 10368, 22752, 21606, 108, 18576], 'label': '31104.fx.216.ik1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.ik1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ik1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186245456
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.il1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.u1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.dn1', '108.e1', '108.gm1', '108.gq1'], 'contains': ['432.iy1', '432.jf1', '432.jn1', '432.jx1', '432.kg1', '432.lb1', '432.ls1', '648.gs1', '648.hi1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [8305, 10368, 22752, 21606, 108, 18576], 'label': '31104.fx.216.il1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.il1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.il1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186245457
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.im1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.do1', '108.h1', '108.gk1', '108.gm1'], 'contains': ['432.iu1', '432.ix1', '432.jn1', '432.jt1', '432.ka1', '432.ki1', '432.ks1', '648.gv1', '648.hj1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [8305, 10368, 22752, 24198, 2628, 18576], 'label': '31104.fx.216.im1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.im1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.im1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186245458
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.in1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.dp1', '108.i1', '108.gk1', '108.gm1'], 'contains': ['432.ix1', '432.iy1', '432.jk1', '432.ka1', '432.kf1', '432.kh1', '432.lf1', '648.gw1', '648.hk1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 10368, 22752, 24198, 2628, 18576], 'label': '31104.fx.216.in1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.in1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.in1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186245459
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '24.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1', '12.i1', '12.v1'], 'contains': ['48.r1', '48.u1', '72.cf1', '72.cg1', '72.ch1', '72.ci1', '96.d1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1, 10368, 12384, 2664, 10924, 18144, 72, 12096], 'label': '31104.fx.24.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.k1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.k1', 'subgroup_fusion': None, 'weyl_group': None}
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id: 186245460
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.io1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.dm1', '108.b1', '108.gn1', '108.gp1'], 'contains': ['432.iz1', '432.jd1', '432.jj1', '432.kk1', '432.km1', '432.ku1', '432.ky1', '648.gt1', '648.hh1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 10368, 12096, 2598, 108, 18576], 'label': '31104.fx.216.io1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.io1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.io1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186245461
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ip1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.dn1', '108.c1', '108.gn1', '108.gp1'], 'contains': ['432.ja1', '432.jd1', '432.jl1', '432.kk1', '432.ko1', '432.la1', '432.lo1', '648.gu1', '648.hi1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [8305, 10368, 12096, 2598, 108, 18576], 'label': '31104.fx.216.ip1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.ip1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ip1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186245462
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.iq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.do1', '108.f1', '108.gj1', '108.gn1'], 'contains': ['432.iv1', '432.iz1', '432.jl1', '432.ju1', '432.kl1', '432.kq1', '432.kw2', '648.gx1', '648.hj1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [8305, 10368, 12096, 6, 2700, 18576], 'label': '31104.fx.216.iq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.iq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.iq1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186245463
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ir1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.dp1', '108.g1', '108.gj1', '108.gn1'], 'contains': ['432.iv1', '432.ja1', '432.jj1', '432.kd1', '432.kl1', '432.kp1', '432.ld2', '648.gy1', '648.hk1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 10368, 12096, 6, 2700, 18576], 'label': '31104.fx.216.ir1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.ir1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ir1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186245464
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.is1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.dq1', '108.h1', '108.gg1', '108.gq1'], 'contains': ['432.jb1', '432.ji1', '432.jn1', '432.ks1', '432.kt1', '432.lj1', '432.lu1', '648.gz1', '648.hl1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [8305, 10368, 22752, 24270, 2628, 18576], 'label': '31104.fx.216.is1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.is1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.is1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186245465
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.it1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.dq1', '108.f1', '108.gh1', '108.gp1'], 'contains': ['432.jc1', '432.jg1', '432.jl1', '432.kw1', '432.ky1', '432.lg1', '432.lr1', '648.ha1', '648.hl1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [8305, 10368, 12096, 78, 2628, 18576], 'label': '31104.fx.216.it1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.it1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.it1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186245466
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.iu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.dr1', '108.g1', '108.gh1', '108.gp1'], 'contains': ['432.jg1', '432.jj1', '432.jm1', '432.ld1', '432.lg1', '432.ll1', '432.lo1', '648.hb1', '648.hm1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 10368, 12096, 78, 2628, 18576], 'label': '31104.fx.216.iu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.iu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.iu1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186245467
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.iv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.dr1', '108.i1', '108.gg1', '108.gq1'], 'contains': ['432.ji1', '432.jk1', '432.jo1', '432.lf1', '432.lj1', '432.ln1', '432.ls1', '648.hc1', '648.hm1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 10368, 22752, 24270, 2628, 18576], 'label': '31104.fx.216.iv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.iv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.iv1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186245468
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.iw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ds1', '108.f1', '108.gj1', '108.go1'], 'contains': ['432.il1', '432.iq1', '432.iv1', '432.jc1', '432.jq1', '432.ke1', '432.kw2', '648.hd1', '648.hn1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [8305, 10368, 12096, 2670, 2700, 18576], 'label': '31104.fx.216.iw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.iw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.iw1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186245469
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ix1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.dt1', '108.g1', '108.gj1', '108.go1'], 'contains': ['432.im1', '432.iq1', '432.iv1', '432.jm1', '432.jp1', '432.kb1', '432.ld2', '648.he1', '648.ho1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 10368, 12096, 2670, 2700, 18576], 'label': '31104.fx.216.ix1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.ix1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ix1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186245470
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '24.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1', '12.i1', '12.q1'], 'contains': ['48.u1', '72.cj1', '72.cl1', '72.cn1', '72.co1', '96.e1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [28981, 1728, 12384, 10368, 31084, 18144, 18216, 2592], 'label': '31104.fx.24.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.l1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.l1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
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id: 186245471
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.iy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ds1', '108.f1', '108.gi1', '108.gp1'], 'contains': ['432.in1', '432.io1', '432.iz1', '432.jg1', '432.jq1', '432.ko1', '432.kw1', '648.hd1', '648.hp1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [8305, 10368, 12096, 2598, 2628, 18576], 'label': '31104.fx.216.iy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.iy1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.iy1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186245472
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.iz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.dt1', '108.g1', '108.gi1', '108.gp1'], 'contains': ['432.in1', '432.it1', '432.ja1', '432.jg1', '432.jp1', '432.km1', '432.ld1', '648.he1', '648.hq1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 10368, 12096, 2598, 2628, 18576], 'label': '31104.fx.216.iz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.iz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.iz1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186245473
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ja1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.du1', '108.b1', '108.go1', '108.gp1'], 'contains': ['432.io1', '432.ip1', '432.jc1', '432.jd1', '432.jp1', '432.ku1', '432.ll1', '648.hf1', '648.hr1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 10368, 12096, 78, 108, 18576], 'label': '31104.fx.216.ja1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.ja1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ja1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186245474
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.jb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.dv1', '108.c1', '108.go1', '108.gp1'], 'contains': ['432.ip1', '432.it1', '432.jd1', '432.jm1', '432.jq1', '432.la1', '432.lr1', '648.hg1', '648.hs1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [8305, 10368, 12096, 78, 108, 18576], 'label': '31104.fx.216.jb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.jb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jb1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186245475
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.jc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ds1', '108.h1', '108.gk1', '108.gq1'], 'contains': ['432.iu1', '432.ix1', '432.jb1', '432.ji1', '432.js1', '432.kg1', '432.ks1', '648.hn1', '648.hp1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [8305, 10368, 22752, 21606, 2628, 18576], 'label': '31104.fx.216.jc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.jc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jc1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186245476
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.jd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.dt1', '108.i1', '108.gk1', '108.gq1'], 'contains': ['432.ix1', '432.iy1', '432.ji1', '432.jo1', '432.jr1', '432.kc1', '432.lf1', '648.ho1', '648.hq1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 10368, 22752, 21606, 2628, 18576], 'label': '31104.fx.216.jd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.jd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jd1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186245477
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.je1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.du1', '108.d1', '108.gq1'], 'contains': ['432.jb1', '432.jf1', '432.jr1', '432.kr1', '432.ln1', '648.hr1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [5713, 10368, 22752, 24270, 108, 18576], 'label': '31104.fx.216.je1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.je1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.je1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186245478
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.jf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dv1', '108.e1', '108.gq1'], 'contains': ['432.jf1', '432.jo1', '432.js1', '432.lb1', '432.lu1', '648.hs1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [8305, 10368, 22752, 24270, 108, 18576], 'label': '31104.fx.216.jf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.jf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jf1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186245479
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.jg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.dw1', '108.h1', '108.gg1', '108.gm1'], 'contains': ['432.jt1', '432.ka1', '432.kg1', '432.ks1', '432.kt1', '432.lj1', '432.lt1', '648.ht1', '648.hv1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [8305, 10368, 22752, 21678, 2628, 18576], 'label': '31104.fx.216.jg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.jg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jg1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186245480
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.jh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.dw1', '108.f1', '108.gh1', '108.gl1'], 'contains': ['432.ju1', '432.jy1', '432.ke1', '432.kw1', '432.kz1', '432.lg1', '432.lq1', '648.ht1', '648.hw1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [8305, 10368, 12096, 2670, 2628, 18576], 'label': '31104.fx.216.jh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.jh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jh1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186245481
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1', '12.h1', '12.v1'], 'contains': ['48.u1', '72.ck1', '72.cm1', '72.cp1', '72.cq1', '96.f1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [18577, 10368, 12384, 12096, 29068, 18144, 18216, 2592], 'label': '31104.fx.24.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.m1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.m1', 'subgroup_fusion': None, 'weyl_group': None}
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id: 186245482
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ji1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.dx1', '108.g1', '108.gh1', '108.gl1'], 'contains': ['432.jy1', '432.kb1', '432.kd1', '432.ld1', '432.lg1', '432.lk1', '432.lp1', '648.hu1', '648.hx1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 10368, 12096, 2670, 2628, 18576], 'label': '31104.fx.216.ji1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.ji1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ji1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186245483
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.jj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.dx1', '108.i1', '108.gg1', '108.gm1'], 'contains': ['432.ka1', '432.kc1', '432.kf1', '432.lf1', '432.lj1', '432.lm1', '432.ls1', '648.hu1', '648.hy1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 10368, 22752, 21678, 2628, 18576], 'label': '31104.fx.216.jj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.jj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jj1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186245484
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.jk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dy1', '108.d1', '108.gm1'], 'contains': ['432.jt1', '432.jx1', '432.kh1', '432.kr1', '432.lm1', '648.hz1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [5713, 10368, 22752, 24198, 108, 18576], 'label': '31104.fx.216.jk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.jk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jk1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186245485
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.jl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dz1', '108.e1', '108.gm1'], 'contains': ['432.jx1', '432.kf1', '432.ki1', '432.lb1', '432.lt1', '648.ia1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [8305, 10368, 22752, 24198, 108, 18576], 'label': '31104.fx.216.jl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.jl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jl1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186245486
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.jm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.dw1', '108.f1', '108.gf1', '108.gn1'], 'contains': ['432.kj1', '432.kl1', '432.ko1', '432.kw2', '432.ky1', '432.lh1', '432.lq1', '648.hv1', '648.hw1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [8305, 10368, 12096, 2598, 2700, 18576], 'label': '31104.fx.216.jm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.jm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jm1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
-
id: 186245487
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.jn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.dx1', '108.g1', '108.gf1', '108.gn1'], 'contains': ['432.kl1', '432.km1', '432.kn1', '432.ld2', '432.lh1', '432.lk1', '432.lo1', '648.hx1', '648.hy1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 10368, 12096, 2598, 2700, 18576], 'label': '31104.fx.216.jn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.jn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jn1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186245488
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.jo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.dy1', '108.b1', '108.gl1', '108.gn1'], 'contains': ['432.ju1', '432.jv1', '432.kj1', '432.kk1', '432.kp1', '432.ku1', '432.lk1', '648.hz1', '648.ib1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 10368, 12096, 6, 108, 18576], 'label': '31104.fx.216.jo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.jo1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jo1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186245489
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.jp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.dz1', '108.c1', '108.gl1', '108.gn1'], 'contains': ['432.jv1', '432.kd1', '432.kk1', '432.kn1', '432.kq1', '432.la1', '432.lq1', '648.ia1', '648.ic1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [8305, 10368, 12096, 6, 108, 18576], 'label': '31104.fx.216.jp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.jp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jp1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186245490
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.jq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.q1', '72.ea1', '72.eb1', '108.ge1'], 'contains': ['432.lw1', '432.mf1', '432.my1', '648.id1', '648.ij1', '864.go1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [24198, 22752, 18576, 36, 20812, 2664], 'label': '31104.fx.216.jq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ge1', 'old_label': '216.jq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jq1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186245491
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.jr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.s1', '72.ee1', '108.gd1'], 'contains': ['432.lv1', '432.mj1', '432.nc1', '648.ie1', '648.ig1', '864.gq1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [24198, 432, 16056, 36, 456, 22752], 'label': '31104.fx.216.jr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.gd1', 'old_label': '216.jr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jr1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186245492
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '24.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.df1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '12.k1', '12.q1', '12.v1'], 'contains': ['48.u1', '72.a1', '72.cx1', '72.cy1', '72.da1', '72.db1', '96.g1'], 'core': '72.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [18576, 10368, 12384, 15552, 12096, 18144, 72, 10924], 'label': '31104.fx.24.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '24.n1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.n1', 'subgroup_fusion': None, 'weyl_group': '432.747'}
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id: 186245493
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.js1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.r1', '72.eb1', '108.gd1'], 'contains': ['432.lv1', '432.mm1', '432.mq1', '648.id1', '648.im1', '864.gp1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [24198, 10368, 18576, 36, 22828, 2664], 'label': '31104.fx.216.js1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.gd1', 'old_label': '216.js1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.js1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
-
id: 186245494
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.jt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.t1', '72.ec1', '72.ed1', '72.ee1', '108.ge1'], 'contains': ['432.lw1', '432.mp1', '432.mt1', '648.ie1', '648.il1', '864.gr1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [24198, 432, 16056, 36, 456, 10368], 'label': '31104.fx.216.jt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ge1', 'old_label': '216.jt1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jt1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186245495
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ju1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.v1', '72.ef1', '108.gd1'], 'contains': ['432.lv1', '432.ni1', '432.nw1', '648.if1', '648.in1', '864.gt1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [20737, 2592, 18576, 36, 16080, 22752], 'label': '31104.fx.216.ju1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.gd1', 'old_label': '216.ju1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ju1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186245496
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.jv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.w1', '72.ef1', '72.eg1', '108.ge1'], 'contains': ['432.lw1', '432.nj1', '432.nx1', '648.if1', '648.in2', '864.gu1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1, 2592, 18576, 36, 16080, 10368], 'label': '31104.fx.216.jv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ge1', 'old_label': '216.jv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jv1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186245497
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.jw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.z1', '72.ef1'], 'contains': ['432.lx1', '432.nm1', '432.oa1', '648.if1', '648.io1', '864.gx1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [20737, 2592, 18576, 36, 16080, 12384], 'label': '31104.fx.216.jw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.jw1', 'old_label': '216.jw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jw1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186245498
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.jx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.eh1', '108.j1', '108.gf1', '108.gj1'], 'contains': ['432.hx1', '432.ie1', '432.iq1', '432.kl1', '432.ly1', '432.md1', '432.nb1', '648.ig1', '648.ih1', '648.ii1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26047, 10368, 12096, 36, 16056, 18576], 'label': '31104.fx.216.jx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.jx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jx1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186245499
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.jy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.co1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ea1', '72.ei1', '108.j1', '108.gi1'], 'contains': ['432.hx1', '432.in1', '432.lz1', '432.me1', '432.ne1', '648.ij1', '648.ik1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [26047, 10368, 12096, 36, 18576, 2592], 'label': '31104.fx.216.jy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '216.jy1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jy1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
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id: 186245500
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.jz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cn1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ec1', '72.eh1', '108.l1', '108.gh1', '108.gi1'], 'contains': ['432.hy1', '432.if1', '432.jg1', '432.jy1', '432.lz1', '432.mh1', '432.mr1', '648.ih1', '648.il1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26047, 22752, 12096, 36, 16056, 18576], 'label': '31104.fx.216.jz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.jz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jz1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245501
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ka1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ed1', '72.eh1', '108.k1'], 'contains': ['432.hz1', '432.ig1', '432.jh1', '432.jz1', '432.ma1', '432.mi1', '432.ms1', '648.ii1', '648.il1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [26047, 22752, 12096, 36, 504, 15984], 'label': '31104.fx.216.ka1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.k1', 'old_label': '216.ka1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ka1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245502
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.kb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ee1', '72.eh1', '108.m1', '108.gg1', '108.gk1'], 'contains': ['432.ia1', '432.ii1', '432.ji1', '432.ka1', '432.mb1', '432.mk1', '432.mw1', '648.ig1', '648.il1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [19135, 10368, 22752, 36, 16056, 18576], 'label': '31104.fx.216.kb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.kb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kb1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186245503
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '24.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '12.s1'], 'contains': ['72.cx1', '72.cy1', '72.cz1', '72.dd1', '72.df1', '96.j1', '96.k1'], 'core': '216.b1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [24268, 16056, 18576, 29904, 12384, 15552, 18144, 10368], 'label': '31104.fx.24.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1', 'old_label': '24.o1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.o1', 'subgroup_fusion': None, 'weyl_group': '864.4679'}
-
id: 186245504
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.kc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ei1', '108.k1', '108.l1', '108.gj1'], 'contains': ['432.hy1', '432.hz1', '432.iv1', '432.iw1', '432.ly1', '432.ml1', '432.mx1', '648.ik1', '648.im1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [26047, 22752, 12096, 36, 2592, 18576], 'label': '31104.fx.216.kc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '216.kc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kc1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
-
id: 186245505
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.kd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.eb1', '72.ei1', '108.m1', '108.gk1'], 'contains': ['432.ia1', '432.ix1', '432.mb1', '432.mo1', '432.na1', '648.ij1', '648.im1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [19135, 10368, 22752, 36, 18576, 2592], 'label': '31104.fx.216.kd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '216.kd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kd1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
-
id: 186245506
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ke1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ef1', '72.ej1', '108.n1', '108.gg1', '108.gk1'], 'contains': ['432.ib1', '432.ij1', '432.ks1', '432.lf1', '432.mb1', '432.nf1', '432.nz1', '648.in1', '648.in2', '648.io1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1, 10368, 22752, 36, 3024, 2592], 'label': '31104.fx.216.ke1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.ke1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ke1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186245507
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.kf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ej1', '108.o1', '108.gf1', '108.gj1'], 'contains': ['432.ic1', '432.ih1', '432.kw2', '432.ld2', '432.ly1', '432.ng1', '432.nt1', '648.in1', '648.ip1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [20737, 22752, 1728, 36, 18576, 2592], 'label': '31104.fx.216.kf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.kf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kf1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186245508
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.kg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.eg1', '72.ej1', '108.o1', '108.gh1', '108.gi1'], 'contains': ['432.ic1', '432.ih1', '432.kw1', '432.ld1', '432.lz1', '432.nh1', '432.nu1', '648.in2', '648.ip1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [20737, 22752, 1728, 36, 3024, 2592], 'label': '31104.fx.216.kg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.kg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kg1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245509
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.kh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ej1', '108.p1'], 'contains': ['432.id1', '432.ik1', '432.kx1', '432.le1', '432.mc1', '432.nl1', '432.nv1', '648.io1', '648.ip1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [20737, 12384, 1728, 36, 18576, 2592], 'label': '31104.fx.216.kh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.p1', 'old_label': '216.kh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kh1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245510
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ki1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cu1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ek1', '108.j1', '108.q1', '108.gh1'], 'contains': ['432.ie1', '432.lg1', '432.lz1', '432.ob1', '432.of1', '648.iq1', '648.is1', '648.it1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [10855, 10368, 12096, 36, 2592, 18576], 'label': '31104.fx.216.ki1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '216.ki1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ki1', 'subgroup_fusion': None, 'weyl_group': '144.154'}
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id: 186245511
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.kj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ek1', '108.l1', '108.r1', '108.gf1'], 'contains': ['432.if1', '432.lh1', '432.ly1', '432.oc1', '432.oe2', '648.ir1', '648.is1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [25975, 22752, 12096, 36, 2592, 18576], 'label': '31104.fx.216.kj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '216.kj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kj1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
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id: 186245512
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.kk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ek1', '108.k1', '108.r1', '108.s1'], 'contains': ['432.ig1', '432.li1', '432.ly1', '432.od1', '432.oe1', '648.ir1', '648.it1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [10495, 22752, 12096, 36, 18576, 2592], 'label': '31104.fx.216.kk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bb1', 'old_label': '216.kk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kk1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186245513
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.kl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ek1', '108.m1', '108.u1', '108.gg1'], 'contains': ['432.ii1', '432.lj1', '432.mb1', '432.og1', '432.oh1', '648.iq1', '648.ir1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [3943, 10368, 22752, 36, 2592, 18576], 'label': '31104.fx.216.kl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '216.kl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kl1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
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id: 186245514
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '24.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.a1', '12.m1', '12.p1', '12.u1'], 'contains': ['72.b1', '72.cv1', '72.cw1', '72.cy1', '72.cz1', '96.m1'], 'core': '72.b1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [76, 16056, 18576, 29904, 22752, 15552, 18144, 10368], 'label': '31104.fx.24.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '24.p1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.p1', 'subgroup_fusion': None, 'weyl_group': '1728.47856'}
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id: 186245515
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.km1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.en1', '108.x1', '108.gj1', '108.gl1'], 'contains': ['432.il1', '432.im1', '432.ju1', '432.kd1', '432.md1', '432.mx1', '432.ng1', '648.iu1', '648.iy1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26485, 12096, 18576, 12138, 2592, 22752], 'label': '31104.fx.216.km1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.km1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.km1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
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id: 186245516
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.kn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.em1', '108.j1', '108.gl1', '108.gp1'], 'contains': ['432.in1', '432.ip1', '432.kk1', '432.lg1', '432.md1', '432.nb1', '432.no2', '648.iv1', '648.iw1', '648.ix1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26047, 10368, 12096, 2628, 16056, 18576], 'label': '31104.fx.216.kn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.kn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kn1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186245517
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ko1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.eo1', '108.x1', '108.gf1', '108.gp1'], 'contains': ['432.io1', '432.it1', '432.ky1', '432.lo1', '432.md1', '432.ng1', '432.oe2', '648.iz1', '648.ja1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26485, 12096, 18576, 12210, 2592, 22752], 'label': '31104.fx.216.ko1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.ko1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ko1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
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id: 186245518
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.kp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ep1', '108.bk1', '108.gf1', '108.gl1'], 'contains': ['432.ir1', '432.is1', '432.lk1', '432.lq1', '432.md1', '432.nt1', '432.oc1', '648.jb1', '648.jc1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 10368, 18576, 14730, 16056, 12096], 'label': '31104.fx.216.kp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.kp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kp1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
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id: 186245635
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.df1', '96.k1'], 'contains': ['864.dp1', '864.dr1', '864.dv1', '1152.q1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [18940, 18144, 29904, 12384, 72], 'label': '31104.fx.288.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.k1', 'old_label': '288.ca1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ca1', 'subgroup_fusion': None, 'weyl_group': '36.11'}
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id: 186245519
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.kq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cy1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.el1', '72.eq1', '108.x1', '108.gi1', '108.go1'], 'contains': ['432.il1', '432.im1', '432.io1', '432.it1', '432.me1', '432.mr1', '432.nh1', '648.jd1', '648.je1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26485, 12096, 18576, 12138, 16056, 22752], 'label': '31104.fx.216.kq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.kq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kq1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245520
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.kr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.bh1', '72.el1', '72.er1', '108.ge1'], 'contains': ['432.mf1', '432.mt1', '432.nj1', '648.jd1', '648.jf1', '864.hf1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [26485, 18576, 2664, 12138, 22752, 28012], 'label': '31104.fx.216.kr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ge1', 'old_label': '216.kr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kr1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186245521
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ks1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.bi1', '72.el1', '72.es1'], 'contains': ['432.mg1', '432.mv1', '432.nk1', '648.jd1', '648.jg1', '864.hg1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [26485, 18576, 2664, 12138, 22752, 29452], 'label': '31104.fx.216.ks1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ks1', 'old_label': '216.ks1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ks1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186245522
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.kt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.et1', '108.j1', '108.y1', '108.go1'], 'contains': ['432.ip1', '432.iq1', '432.me1', '432.np1', '432.of1', '648.jh1', '648.ji1', '648.ji2'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [10855, 10368, 12096, 16092, 2592, 18576], 'label': '31104.fx.216.kt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '216.kt1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kt1', 'subgroup_fusion': None, 'weyl_group': '288.977'}
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id: 186245523
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ku1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.z1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.bj1', '72.eu1', '108.gd1'], 'contains': ['432.mj1', '432.mq1', '432.ni1', '648.iu1', '648.jk1', '864.hi1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [10405, 2592, 18576, 12138, 22752, 16080], 'label': '31104.fx.216.ku1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.gd1', 'old_label': '216.ku1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ku1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186245524
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.kv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.em1', '108.l1', '108.gn1', '108.go1'], 'contains': ['432.iv1', '432.jd1', '432.jv1', '432.lh1', '432.mh1', '432.mr1', '432.np1', '648.iw1', '648.jj1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26047, 22752, 12096, 2628, 16056, 18576], 'label': '31104.fx.216.kv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.kv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kv1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186245525
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '24.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.e1', '12.x1'], 'contains': ['48.v1', '48.w1', '48.y1', '72.ea1', '72.eb1', '72.ei1', '96.q1'], 'core': '576.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [26047, 2592, 12096, 36, 15984, 10368, 22752, 5712], 'label': '31104.fx.24.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.x1', 'old_label': '24.q1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.q1', 'subgroup_fusion': None, 'weyl_group': '2592.jb'}
-
id: 186245526
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.kw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.em1', '108.k1'], 'contains': ['432.iw1', '432.je1', '432.jw1', '432.li1', '432.mi1', '432.ms1', '432.nq1', '648.ix1', '648.jj1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [26047, 22752, 12096, 18612, 504, 15984], 'label': '31104.fx.216.kw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.k1', 'old_label': '216.kw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kw1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245527
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.kx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.em1', '108.m1', '108.gm1', '108.gq1'], 'contains': ['432.ix1', '432.jf1', '432.jx1', '432.lj1', '432.mk1', '432.mw1', '432.nr1', '648.iv1', '648.jj1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [19135, 10368, 22752, 2628, 16056, 18576], 'label': '31104.fx.216.kx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.kx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kx1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186245528
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ky1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.en1', '72.eu1', '108.bb1', '108.gk1', '108.gm1'], 'contains': ['432.iu1', '432.iy1', '432.jt1', '432.kf1', '432.mk1', '432.na1', '432.nf1', '648.iu1', '648.jl1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26485, 10368, 18576, 12138, 2592, 22752], 'label': '31104.fx.216.ky1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.ky1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ky1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
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id: 186245529
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.kz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.db1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.en1', '72.ev1', '108.bc1', '108.gi1', '108.gn1'], 'contains': ['432.iz1', '432.ja1', '432.kj1', '432.kn1', '432.mh1', '432.ne1', '432.nh1', '648.iy1', '648.jl1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [26485, 10368, 12096, 12138, 2592, 18576], 'label': '31104.fx.216.kz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '216.kz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kz1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186245530
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.la1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.eo1', '108.bb1', '108.gg1', '108.gq1'], 'contains': ['432.jb1', '432.jo1', '432.kt1', '432.ls1', '432.mk1', '432.nf1', '432.oh1', '648.iz1', '648.jm1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26485, 10368, 18576, 12210, 2592, 22752], 'label': '31104.fx.216.la1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.la1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.la1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
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id: 186245531
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.lb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ec1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.eo1', '108.bc1', '108.gh1', '108.go1'], 'contains': ['432.jc1', '432.jm1', '432.kz1', '432.lp1', '432.mh1', '432.nh1', '432.of1', '648.ja1', '648.jm1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [26485, 10368, 12096, 12210, 2592, 18576], 'label': '31104.fx.216.lb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '216.lb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.lb1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186245532
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.lc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ej1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ep1', '108.bk1', '108.gh1', '108.gn1'], 'contains': ['432.jj1', '432.jl1', '432.lk1', '432.lq1', '432.mh1', '432.nu1', '432.ob1', '648.jb1', '648.jo1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 10368, 18576, 12210, 2592, 12096], 'label': '31104.fx.216.lc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.lc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.lc1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245533
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ld1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ep1', '108.bl1', '108.gg1', '108.gm1'], 'contains': ['432.jk1', '432.jn1', '432.lm1', '432.lt1', '432.mk1', '432.nz1', '432.og1', '648.jc1', '648.jo1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [5713, 10368, 22752, 12210, 2592, 18576], 'label': '31104.fx.216.ld1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '216.ld1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ld1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186245534
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.le1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cz1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ew1', '72.ex1', '108.bk1', '108.gi1', '108.go1'], 'contains': ['432.ir1', '432.is1', '432.jp1', '432.jq1', '432.me1', '432.mh1', '432.nu1', '648.jn1', '648.jp1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 10368, 18576, 12138, 2592, 12096], 'label': '31104.fx.216.le1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.le1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.le1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245535
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.lf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.eq1', '72.er1', '72.es1', '108.bb1', '108.gk1', '108.gq1'], 'contains': ['432.iu1', '432.iy1', '432.jb1', '432.jo1', '432.mo1', '432.mw1', '432.nf1', '648.jd1', '648.jr1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26485, 10368, 18576, 12138, 16056, 22752], 'label': '31104.fx.216.lf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.lf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.lf1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
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id: 186245536
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '24.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.a1', '12.x1'], 'contains': ['48.v1', '48.x1', '48.z1', '72.ec1', '72.ed1', '72.ee1', '72.eh1', '96.r1'], 'core': '576.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [26047, 24768, 22752, 36, 12096, 18576, 16056, 18148], 'label': '31104.fx.24.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.x1', 'old_label': '24.r1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.r1', 'subgroup_fusion': None, 'weyl_group': '2592.jb'}
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id: 186245694
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.fe1', '96.bb1'], 'contains': ['576.bd1', '576.be1', '576.cc1', '864.hy1', '864.if1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 576, 'diagramx': None, 'generators': [1, 10368, 22758, 28464, 12096], 'label': '31104.fx.288.ea1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.ea1', 'old_label': '288.ea1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ea1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
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id: 186245537
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.lg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.eq1', '108.bc1', '108.gj1', '108.gp1'], 'contains': ['432.iz1', '432.ja1', '432.jc1', '432.jm1', '432.ml1', '432.nb1', '432.ng1', '648.je1', '648.jr1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [26485, 10368, 12096, 12138, 16056, 18576], 'label': '31104.fx.216.lg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '216.lg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.lg1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186245538
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.lh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.bc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.bn1', '72.er1', '108.gd1'], 'contains': ['432.mm1', '432.nc1', '432.ni1', '648.jf1', '648.jr1', '864.ho1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [26485, 18576, 2664, 12138, 28012, 10368], 'label': '31104.fx.216.lh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.dj1', 'old_label': '216.lh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.lh1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186245539
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.li1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.bo1', '72.es1'], 'contains': ['432.mn1', '432.nd1', '432.nk2', '648.jg1', '648.jr1', '864.hp1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [13861, 2592, 18576, 6, 19536, 22752], 'label': '31104.fx.216.li1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.es1', 'old_label': '216.li1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.li1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186245540
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.lj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.et1', '108.k1', '108.bd1', '108.be1'], 'contains': ['432.je1', '432.jh1', '432.ml1', '432.no1', '432.oe1', '648.ji1', '648.js1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [10495, 22752, 12096, 15588, 18576, 2592], 'label': '31104.fx.216.lj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bb1', 'old_label': '216.lj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.lj1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186245541
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.lj2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.et1', '108.l1', '108.bd1', '108.gp1'], 'contains': ['432.jd1', '432.jg1', '432.ml1', '432.no2', '432.oe2', '648.ji2', '648.js1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [25975, 22752, 12096, 108, 2592, 18576], 'label': '31104.fx.216.lj2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '216.lj2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.lj2', 'subgroup_fusion': None, 'weyl_group': '288.958'}
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id: 186245542
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.lk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.et1', '108.m1', '108.bf1', '108.gq1'], 'contains': ['432.jf1', '432.ji1', '432.mo1', '432.nr1', '432.oh1', '648.jh1', '648.js1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [3943, 10368, 22752, 16092, 2592, 18576], 'label': '31104.fx.216.lk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '216.lk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.lk1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
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id: 186245543
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ll1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ew1', '108.bk1', '108.gj1', '108.gp1'], 'contains': ['432.jj1', '432.jl1', '432.jp1', '432.jq1', '432.md1', '432.ml1', '432.nt1', '648.jn1', '648.jt1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 10368, 18576, 12138, 16056, 12096], 'label': '31104.fx.216.ll1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.ll1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ll1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
-
id: 186245544
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.lm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.bu1', '72.eu1', '72.ev1', '108.ge1'], 'contains': ['432.mp1', '432.my1', '432.nj1', '648.jk1', '648.jl1', '864.hv1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [10405, 2592, 18576, 12138, 16080, 10368], 'label': '31104.fx.216.lm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.dj1', 'old_label': '216.lm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.lm1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
-
id: 186245545
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ln1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.bq1', '72.ey1', '108.gd1'], 'contains': ['432.mj1', '432.mm1', '432.nw1', '648.jq1', '648.jt1', '864.hr1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1, 2592, 18576, 12138, 5712, 22752], 'label': '31104.fx.216.ln1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.gd1', 'old_label': '216.ln1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ln1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186245546
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.lo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ew1', '72.ey1', '108.bl1', '108.gk1', '108.gq1'], 'contains': ['432.jk1', '432.jn1', '432.jr1', '432.js1', '432.mk1', '432.mo1', '432.nz1', '648.jp1', '648.jt1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [5713, 10368, 22752, 12138, 2592, 18576], 'label': '31104.fx.216.lo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '216.lo1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.lo1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186245547
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '24.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.g1', '12.x1'], 'contains': ['48.v1', '48.ba1', '48.bb1', '72.ef1', '72.eg1', '72.ej1', '96.t1'], 'core': '576.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [1, 22752, 10368, 36, 12096, 2592, 18576, 5712], 'label': '31104.fx.24.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.x1', 'old_label': '24.s1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.s1', 'subgroup_fusion': None, 'weyl_group': '2592.jb'}
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id: 186245548
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.lp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.bv1', '72.ex1', '72.ey1', '108.ge1'], 'contains': ['432.mf1', '432.mp1', '432.nx1', '648.jp1', '648.jq1', '864.hw1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [1, 2592, 18576, 12138, 5712, 10368], 'label': '31104.fx.216.lp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.di1', 'old_label': '216.lp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.lp1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
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id: 186245549
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.lq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ez1', '108.bb1', '108.gg1', '108.gm1'], 'contains': ['432.jt1', '432.kf1', '432.kt1', '432.ls1', '432.mw1', '432.nf1', '432.og1', '648.ju1', '648.jx1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26485, 10368, 18576, 14730, 16056, 22752], 'label': '31104.fx.216.lq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.lq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.lq1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
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id: 186245550
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.lr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.eb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ez1', '108.x1', '108.gh1', '108.gn1'], 'contains': ['432.ju1', '432.kd1', '432.ky1', '432.lo1', '432.mr1', '432.nh1', '432.ob1', '648.ju1', '648.jy1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26485, 12096, 18576, 14730, 16056, 22752], 'label': '31104.fx.216.lr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.lr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.lr1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245551
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ls1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.fa1', '108.bx1', '108.gh1', '108.go1'], 'contains': ['432.kb1', '432.ke1', '432.ll1', '432.lr1', '432.mr1', '432.nu1', '432.of1', '648.jv1', '648.jz1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 10368, 12096, 78, 2592, 18576], 'label': '31104.fx.216.ls1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.ls1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ls1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186245552
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.lt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.fa1', '108.bt1', '108.gg1', '108.gq1'], 'contains': ['432.kc1', '432.kg1', '432.ln1', '432.lu1', '432.mw1', '432.nz1', '432.oh1', '648.jv1', '648.ka1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 10368, 22752, 78, 2592, 18576], 'label': '31104.fx.216.lt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.lt1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.lt1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186245553
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.lu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.fc1', '108.l1', '108.bm1', '108.gl1'], 'contains': ['432.jv1', '432.jy1', '432.mx1', '432.no2', '432.oc1', '648.jw1', '648.kf1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [26047, 22752, 12096, 108, 2592, 18576], 'label': '31104.fx.216.lu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '216.lu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.lu1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
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id: 186245554
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.lv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.fc1', '108.k1', '108.bm1', '108.bn1'], 'contains': ['432.jw1', '432.jz1', '432.mx1', '432.no1', '432.od1', '648.jw1', '648.kg1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26047, 22752, 12096, 15588, 18576, 2592], 'label': '31104.fx.216.lv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bb1', 'old_label': '216.lv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.lv1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186245555
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.lw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.fc1', '108.m1', '108.bo1', '108.gm1'], 'contains': ['432.jx1', '432.ka1', '432.na1', '432.nr1', '432.og1', '648.jw1', '648.ke1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [19135, 10368, 22752, 16092, 2592, 18576], 'label': '31104.fx.216.lw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '216.lw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.lw1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
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id: 186245556
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.lx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ez1', '108.bc1', '108.gf1', '108.gl1'], 'contains': ['432.kj1', '432.kn1', '432.kz1', '432.lp1', '432.nb1', '432.ng1', '432.oc1', '648.jx1', '648.jy1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [26485, 10368, 12096, 14730, 16056, 18576], 'label': '31104.fx.216.lx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '216.lx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.lx1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186245557
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ly1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.fa1', '108.bx1', '108.gf1', '108.gp1'], 'contains': ['432.km1', '432.ko1', '432.ll1', '432.lr1', '432.nb1', '432.nt1', '432.oe2', '648.jz1', '648.ka1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 10368, 12096, 2598, 16056, 18576], 'label': '31104.fx.216.ly1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.ly1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ly1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186245558
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '4.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': ['7776.y1', '7776.bb1', '7776.bd1', '7776.bc1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '2.c1'], 'contains': ['8.a1', '12.q1', '12.r1', '12.s1', '12.t1', '12.u1', '16.b1'], 'core': '4.d1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [10405, 18144, 22752, 10368, 15552, 12460, 1728, 15984, 15624, 16080], 'label': '31104.fx.4.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': ['2.b1', '2.c1'], 'normal_contains': ['8.a1'], 'normalizer': '1.a1', 'old_label': '4.d1', 'projective_image': '31104.fx', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.d1', 'subgroup_fusion': None, 'weyl_group': '3456.di'}
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id: 186245559
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '24.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.h1', '12.x1'], 'contains': ['48.w1', '48.z1', '48.ba1', '72.el1', '72.eq1', '72.er1', '72.es1', '96.u1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [10405, 22752, 10368, 6, 1728, 2592, 18576, 28176], 'label': '31104.fx.24.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.x1', 'old_label': '24.t1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.t1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
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id: 186245560
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.lz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.bw1', '72.fb1', '72.fd1', '108.ge1'], 'contains': ['432.mt1', '432.my1', '432.nx1', '648.kc1', '648.kh1', '864.hx1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1, 2592, 18576, 6, 5712, 10368], 'label': '31104.fx.216.lz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ge1', 'old_label': '216.lz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.lz1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186245561
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ma1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.bx1', '72.fb1', '72.fe1'], 'contains': ['432.mu1', '432.mz1', '432.ny1', '648.kd1', '648.kh1', '864.hy1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [1, 2592, 18576, 22758, 28464, 10368], 'label': '31104.fx.216.ma1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ma1', 'old_label': '216.ma1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ma1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186245562
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.mb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.fb1', '72.ff1', '108.bt1', '108.gk1', '108.gm1'], 'contains': ['432.kc1', '432.kg1', '432.kh1', '432.ki1', '432.mw1', '432.na1', '432.nz1', '648.kb1', '648.kh1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 10368, 22752, 6, 2592, 18576], 'label': '31104.fx.216.mb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.mb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.mb1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
-
id: 186245563
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.mc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.cd1', '72.fb1', '108.gd1'], 'contains': ['432.mq1', '432.nc1', '432.nw1', '648.kb1', '648.kc1', '648.kd1', '864.ie1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1, 2592, 18576, 6, 5712, 22752], 'label': '31104.fx.216.mc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.gd1', 'old_label': '216.mc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.mc1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
-
id: 186245564
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.md1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ff1', '108.bx1', '108.gj1', '108.gl1'], 'contains': ['432.kb1', '432.ke1', '432.kp1', '432.kq1', '432.mx1', '432.nb1', '432.nt1', '648.kb1', '648.ki1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 10368, 12096, 6, 16056, 18576], 'label': '31104.fx.216.md1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.md1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.md1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
-
id: 186245565
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.me1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.fc1', '108.j1', '108.bu1', '108.gn1'], 'contains': ['432.kk1', '432.kl1', '432.ne1', '432.np1', '432.ob1', '648.ke1', '648.kf1', '648.kg1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [26047, 10368, 12096, 16092, 2592, 18576], 'label': '31104.fx.216.me1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '216.me1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.me1', 'subgroup_fusion': None, 'weyl_group': '288.977'}
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id: 186245566
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.mf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.fd1', '72.fe1', '72.ff1', '108.bx1', '108.gi1', '108.gn1'], 'contains': ['432.km1', '432.ko1', '432.kp1', '432.kq1', '432.mr1', '432.ne1', '432.nu1', '648.kh1', '648.ki1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 10368, 12096, 6, 2592, 18576], 'label': '31104.fx.216.mf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.mf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.mf1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186245567
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.mg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.fg1', '108.n1', '108.gm1', '108.gq1'], 'contains': ['432.kr1', '432.ks1', '432.lb1', '432.lf1', '432.nf1', '432.nr1', '432.nz1', '648.kj1', '648.kj2', '648.kk1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1, 10368, 22752, 15588, 3024, 2592], 'label': '31104.fx.216.mg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.mg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.mg1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186245568
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.mh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.fg1', '108.o1', '108.gl1', '108.gp1'], 'contains': ['432.ku1', '432.kw1', '432.la1', '432.ld1', '432.ng1', '432.no2', '432.nt1', '648.kj1', '648.kl1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1, 10368, 1728, 15588, 3024, 2592], 'label': '31104.fx.216.mh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.mh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.mh1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186245569
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.mi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.fg1', '108.o1', '108.gn1', '108.go1'], 'contains': ['432.ku1', '432.kw2', '432.la1', '432.ld2', '432.nh1', '432.np1', '432.nu1', '648.kj2', '648.kl1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1, 10368, 1728, 15588, 18576, 2592], 'label': '31104.fx.216.mi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.mi1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.mi1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186245570
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '24.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.i1', '12.x1'], 'contains': ['48.x1', '48.y1', '48.ba1', '72.en1', '72.eu1', '72.ev1', '96.v1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [26485, 12096, 22752, 6, 28012, 18576, 2664, 10368], 'label': '31104.fx.24.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.x1', 'old_label': '24.u1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.u1', 'subgroup_fusion': None, 'weyl_group': '864.4000'}
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id: 186245571
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.mj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.fg1', '108.p1'], 'contains': ['432.kv1', '432.kx1', '432.lc1', '432.le1', '432.nl1', '432.ns1', '432.nv1', '648.kk1', '648.kl1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [20737, 12384, 1728, 15588, 18576, 2592], 'label': '31104.fx.216.mj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.p1', 'old_label': '216.mj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.mj1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245572
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.mk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.fh1', '108.q1', '108.y1', '108.bu1'], 'contains': ['432.np1', '432.ob1', '432.of1', '648.km1', '648.ko1', '648.kp1', '648.kp2'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [10495, 10368, 12096, 16092, 18576, 2592], 'label': '31104.fx.216.mk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.ba1', 'old_label': '216.mk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.mk1', 'subgroup_fusion': None, 'weyl_group': '144.196'}
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id: 186245573
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ml1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.fh1', '108.r1', '108.be1', '108.bm1'], 'contains': ['432.no1', '432.oc1', '432.oe1', '648.kn1', '648.ko1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [10423, 22752, 12096, 15588, 15984, 18576], 'label': '31104.fx.216.ml1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bb1', 'old_label': '216.ml1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ml1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186246098
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ik1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dk1', '216.v1', '216.kh1'], 'contains': ['864.ei1', '864.fz1', '864.ga1', '1296.gh1', '1296.gk1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [8209, 12384, 36, 2592, 1728], 'label': '31104.fx.432.ik1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.p1', 'old_label': '432.ik1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ik1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245574
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.mm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.fh1', '108.r1', '108.bd1', '108.bn1'], 'contains': ['432.no1', '432.od1', '432.oe2', '648.kn1', '648.kp1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [25975, 22752, 12096, 15588, 2592, 18576], 'label': '31104.fx.216.mm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bb1', 'old_label': '216.mm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.mm1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186245575
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.mm2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.fh1', '108.s1', '108.bd1', '108.bm1'], 'contains': ['432.no2', '432.od1', '432.oe1', '648.kn1', '648.kp2'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [10495, 22752, 12096, 108, 2592, 18576], 'label': '31104.fx.216.mm2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bb1', 'old_label': '216.mm2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.mm2', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186245576
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.mn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.fh1', '108.u1', '108.bf1', '108.bo1'], 'contains': ['432.nr1', '432.og1', '432.oh1', '648.km1', '648.kn1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [3583, 10368, 22752, 16092, 18576, 2592], 'label': '31104.fx.216.mn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bc1', 'old_label': '216.mn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.mn1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186245577
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '243.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['81.a1', '81.b1', '81.c1'], 'contains': ['486.a1', '486.b1', '486.c1', '486.d1', '486.e1', '486.f1', '486.g1', '486.h1', '486.i1', '486.j1', '486.k1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [5713, 24198, 36, 15552], 'label': '31104.fx.243.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '243.a1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '243.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
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id: 186245578
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.a1', '144.b1', '144.c1', '144.d1', '144.e1', '144.bg1', '144.da1'], 'contains': ['576.b1', '576.i1', '864.a1', '864.b1', '864.c1', '864.d1', '864.e1', '864.f1', '864.g1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [16056, 10368, 15552, 12096, 22752], 'label': '31104.fx.288.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '288.a1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 186245579
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ck1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bt1', '96.a1', '144.f1', '144.h1', '144.bl1'], 'contains': ['576.c1', '576.m1', '576.bx1', '864.h1', '864.i1', '864.j1', '864.l1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [36, 10368, 3096, 10924, 2016], 'label': '31104.fx.288.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bj1', 'old_label': '288.b1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.b1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
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id: 186245580
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bu1', '96.a1', '144.g1', '144.i1', '144.bo1'], 'contains': ['576.e1', '576.o1', '576.by1', '864.j1', '864.m1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [36, 12384, 18648, 556, 12096], 'label': '31104.fx.288.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bn1', 'old_label': '288.c1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.c1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
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id: 186245581
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '24.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.l1', '12.x1'], 'contains': ['48.w1', '48.x1', '48.bb1', '72.ew1', '72.ex1', '72.ey1', '96.y1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [1, 22752, 10368, 12138, 5712, 2592, 18576, 12096], 'label': '31104.fx.24.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.x1', 'old_label': '24.v1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.v1', 'subgroup_fusion': None, 'weyl_group': '2592.jb'}
-
id: 186245582
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bv1', '96.a1', '144.bo1'], 'contains': ['576.f1', '576.o1', '576.by2', '864.j1', '864.n1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [36, 12384, 3096, 556, 12096], 'label': '31104.fx.288.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.bo1', 'old_label': '288.d1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.d1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
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id: 186245583
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.a1', '144.a1', '144.j1', '144.k1', '144.v1', '144.bq1'], 'contains': ['576.a1', '576.b1', '576.bz1', '864.k1', '864.l1', '864.m1', '864.n1', '864.o1'], 'core': '576.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [36, 2016, 18144, 12096, 10368], 'label': '31104.fx.288.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '288.e1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.e1', 'subgroup_fusion': None, 'weyl_group': '324.124'}
-
id: 186245584
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.b1', '144.b1', '144.j1', '144.m1', '144.n1', '144.o1', '144.y1', '144.br1'], 'contains': ['576.b1', '576.bm1', '864.p1', '864.q1', '864.t1', '864.u1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [10405, 1728, 18144, 22752, 10368], 'label': '31104.fx.288.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bc1', 'old_label': '288.f1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.f1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186245585
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.by1', '96.b1', '144.f1', '144.l1', '144.bs1'], 'contains': ['576.c1', '576.bn1', '864.p1', '864.r1', '864.v1', '864.w1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [10405, 12940, 15552, 22752, 10368], 'label': '31104.fx.288.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bj1', 'old_label': '288.g1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.g1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186245586
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bz1', '96.b1', '144.bv1'], 'contains': ['576.d1', '576.bp1', '864.p1', '864.s1', '864.x1', '864.y1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [10405, 29404, 18144, 22752, 10368], 'label': '31104.fx.288.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.bv1', 'old_label': '288.h1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.h1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186245587
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ca1', '96.b1', '144.g1', '144.p1', '144.cb1'], 'contains': ['576.e1', '576.bu1', '864.t1', '864.w1', '864.x1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [10405, 12384, 15552, 12940, 1728], 'label': '31104.fx.288.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.d1', 'old_label': '288.i1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.i1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245588
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ck1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cb1', '96.c1', '144.l1', '144.r1', '144.bl1'], 'contains': ['576.c1', '576.bx1', '864.z1', '864.ba1', '864.bb1', '864.bi1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [15588, 10368, 3096, 10924, 2016], 'label': '31104.fx.288.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bj1', 'old_label': '288.j1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.j1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
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id: 186245589
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cc1', '96.c1', '144.p1', '144.q1', '144.bo1'], 'contains': ['576.e1', '576.by2', '864.bb1', '864.bj1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [15588, 12384, 18648, 556, 12096], 'label': '31104.fx.288.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bn1', 'old_label': '288.k1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.k1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
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id: 186245590
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cd1', '96.c1', '144.bo1'], 'contains': ['576.f1', '576.by1', '576.by2', '864.bb1', '864.bk1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [18684, 12384, 3096, 556, 12096], 'label': '31104.fx.288.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.bo1', 'old_label': '288.l1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.l1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
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id: 186245591
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.c1', '144.d1', '144.m1', '144.s1', '144.v1', '144.z1', '144.cj1'], 'contains': ['576.b1', '576.bz1', '576.ca1', '864.bc1', '864.bc2', '864.bd1', '864.be1', '864.bf1', '864.bg1', '864.bg2'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [3132, 2016, 18144, 12096, 10368], 'label': '31104.fx.288.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '288.m1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.m1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
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id: 186245592
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '24.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.n1', '12.x1'], 'contains': ['48.y1', '48.z1', '48.bb1', '72.fb1', '72.fd1', '72.fe1', '72.ff1', '96.bb1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [1, 22752, 10368, 6, 12096, 2592, 18576, 5712], 'label': '31104.fx.24.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.x1', 'old_label': '24.w1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.w1', 'subgroup_fusion': None, 'weyl_group': '2592.jb'}
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id: 186245593
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.c1', '144.d1', '144.n1', '144.t1', '144.z1', '144.bq1'], 'contains': ['576.b1', '576.bz1', '864.bh1', '864.bi1', '864.bj1', '864.bk1', '864.bl1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108, 2016, 18144, 12096, 10368], 'label': '31104.fx.288.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '288.n1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.n1', 'subgroup_fusion': None, 'weyl_group': '324.124'}
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id: 186245594
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.a1', '144.c1', '144.o1', '144.u1', '144.z1', '144.ba1', '144.cj1'], 'contains': ['576.b1', '576.ca1', '864.bm1', '864.bm2', '864.bn1', '864.bo1', '864.bp1', '864.bq1', '864.bq2'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [18612, 2016, 18144, 12096, 10368], 'label': '31104.fx.288.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '288.o1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.o1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
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id: 186245595
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.d1', '144.e1', '144.j1', '144.m1', '144.t1', '144.u1', '144.bb1', '144.cm1'], 'contains': ['576.b1', '576.cd1', '864.br1', '864.bs1', '864.bt1', '864.bv1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1, 10368, 18144, 12096, 22752], 'label': '31104.fx.288.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bc1', 'old_label': '288.p1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.p1', 'subgroup_fusion': None, 'weyl_group': '72.49'}
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id: 186245596
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cg1', '96.d1', '144.g1', '144.q1', '144.cn1'], 'contains': ['576.e1', '576.ce1', '864.bs1', '864.bx1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [1, 12384, 15552, 1728, 556], 'label': '31104.fx.288.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bn1', 'old_label': '288.q1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.q1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
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id: 186245597
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ch1', '96.d1', '144.cp1'], 'contains': ['576.g1', '576.cf1', '864.bs1', '864.by1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [1, 12384, 15552, 1728, 10924], 'label': '31104.fx.288.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.cp1', 'old_label': '288.r1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.r1', 'subgroup_fusion': None, 'weyl_group': '108.25'}
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id: 186245598
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ci1', '96.d1', '144.f1', '144.r1', '144.ct1'], 'contains': ['576.c1', '576.ci1', '864.bu1', '864.bv1', '864.bw1', '864.bx1', '864.by1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [1, 12384, 15552, 10924, 22752], 'label': '31104.fx.288.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.d1', 'old_label': '288.s1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.s1', 'subgroup_fusion': None, 'weyl_group': '648.610'}
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id: 186245599
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.e1', '144.b1', '144.k1', '144.s1', '144.t1', '144.u1', '144.bd1', '144.br1'], 'contains': ['576.b1', '864.bz1', '864.ce1', '864.cg1', '864.ch1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [26029, 1728, 22752, 10368, 18144], 'label': '31104.fx.288.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bc1', 'old_label': '288.t1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.t1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186245600
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.f1', '144.e1', '144.k1', '144.n1', '144.o1', '144.s1', '144.bf1', '144.cm1'], 'contains': ['576.b1', '864.ca1', '864.cf1', '864.ci1', '864.cj1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [15625, 10368, 12096, 18144, 22752], 'label': '31104.fx.288.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bc1', 'old_label': '288.u1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.u1', 'subgroup_fusion': None, 'weyl_group': '72.49'}
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id: 186245601
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cl1', '96.e1', '144.h1', '144.r1', '144.bs1'], 'contains': ['576.c1', '864.cb1', '864.ce1', '864.ck1', '864.cm1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [10909, 31084, 22752, 10368, 15552], 'label': '31104.fx.288.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bj1', 'old_label': '288.v1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.v1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186245602
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cm1', '96.f1', '144.h1', '144.l1', '144.ct1'], 'contains': ['576.c1', '864.cc1', '864.cf1', '864.cl1', '864.cn1', '864.co1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [505, 12384, 15552, 29068, 22752], 'label': '31104.fx.288.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.d1', 'old_label': '288.w1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.w1', 'subgroup_fusion': None, 'weyl_group': '648.610'}
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id: 186245603
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '27.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1'], 'contains': ['54.o1', '54.p1', '54.bl1', '54.bs1', '54.bz1', '81.a1', '432.oi1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [20737, 15552, 16080, 16056, 24198, 12460, 18144, 18576, 36], 'label': '31104.fx.27.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '27.a1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.a1', 'subgroup_fusion': None, 'weyl_group': '576.8654'}
-
id: 186245604
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cn1', '96.e1', '144.bv1'], 'contains': ['576.d1', '864.cd1', '864.ce1', '864.cp1', '864.cq1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [26029, 13852, 22752, 10368, 18144], 'label': '31104.fx.288.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.bv1', 'old_label': '288.x1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.x1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186245605
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.co1', '96.e1', '144.i1', '144.q1', '144.cb1'], 'contains': ['576.e1', '864.cg1', '864.cm1', '864.cp1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [10909, 12384, 15552, 31084, 1728], 'label': '31104.fx.288.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.d1', 'old_label': '288.y1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.y1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245606
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cp1', '96.f1', '144.i1', '144.p1', '144.cn1'], 'contains': ['576.e1', '864.ci1', '864.cn1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [505, 12384, 1728, 15552, 18700], 'label': '31104.fx.288.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bn1', 'old_label': '288.z1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.z1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
-
id: 186245607
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cq1', '96.f1', '144.cp1'], 'contains': ['576.g1', '864.ci1', '864.co1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [505, 12384, 1728, 15552, 29068], 'label': '31104.fx.288.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.cp1', 'old_label': '288.ba1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ba1', 'subgroup_fusion': None, 'weyl_group': '108.25'}
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id: 186245608
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.v1', '144.w1', '144.x1', '144.y1', '144.z1', '144.ba1', '144.bb1', '144.bc1', '144.bd1', '144.be1', '144.bf1', '144.bg1', '144.da1'], 'contains': ['576.b1', '576.i1', '864.cr1', '864.cs1', '864.ct1', '864.cu1', '864.cv1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [18144, 10368, 16056, 12096, 22752], 'label': '31104.fx.288.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '288.bb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bb1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 186245609
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.cr1', '96.i1', '144.bk1', '144.by1', '144.ck1'], 'contains': ['864.cw1', '864.da1', '864.de1', '1152.b1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [5260, 15552, 12096, 22752, 18648], 'label': '31104.fx.288.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '288.bc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bc1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186245610
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.cs1', '96.i1', '144.cl1'], 'contains': ['864.cw1', '864.db1', '864.de1', '1152.c1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [12096, 15552, 15628, 22752, 18648], 'label': '31104.fx.288.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.s1', 'old_label': '288.bd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bd1', 'subgroup_fusion': None, 'weyl_group': '72.42'}
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id: 186245611
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ct1', '96.l1', '144.cr1'], 'contains': ['864.cx1', '864.cy1', '864.cz1', '864.db1', '864.dw1', '864.dx1', '864.dy1', '864.dz1', '864.eb1', '864.ec1', '864.ee1', '864.ee2', '1152.d1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [76, 15552, 28464, 10368, 18648], 'label': '31104.fx.288.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.t1', 'old_label': '288.be1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.be1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186245612
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.cu1', '96.l1', '144.bh1', '144.bz1', '144.cs1'], 'contains': ['864.cx1', '864.cy1', '864.cz1', '864.da1', '864.dw1', '864.dy1', '864.ea1', '864.ec1', '864.ed1', '1152.e1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [20812, 15552, 5712, 22752, 18648], 'label': '31104.fx.288.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1', 'old_label': '288.bf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bf1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186245613
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.cv1', '96.m1', '144.ca1'], 'contains': ['864.da1', '864.dc1', '864.dd1', '864.de2', '1152.f1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [24268, 15552, 16080, 10368, 18648], 'label': '31104.fx.288.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.o1', 'old_label': '288.bg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bg1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
-
id: 186245614
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '27.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['9.a1', '9.c1'], 'contains': ['54.r1', '54.s1', '54.v1', '54.bj1', '54.bn1', '54.bq1', '54.cd1', '81.a1', '81.c1', '108.gd1'], 'core': '648.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [20737, 15552, 22752, 16056, 24198, 16080, 2592, 432, 36], 'label': '31104.fx.27.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '27.b1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.b1', 'subgroup_fusion': None, 'weyl_group': '1152.155790'}
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id: 186245615
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.cw1', '96.m1'], 'contains': ['864.db1', '864.dc1', '864.dd1', '864.de2', '1152.g1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [7728, 15552, 24268, 10368, 18648], 'label': '31104.fx.288.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.m1', 'old_label': '288.bh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bh1', 'subgroup_fusion': None, 'weyl_group': '36.11'}
-
id: 186245616
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.g1', '96.h1', '96.i1', '144.bq1', '144.br1', '144.cj1', '144.cm1', '144.da1'], 'contains': ['576.b1', '864.cw1', '864.df1', '864.dg1', '864.dh1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [3096, 10368, 15552, 12096, 22752], 'label': '31104.fx.288.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '288.bi1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bi1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
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id: 186245617
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cx1', '96.g1', '96.j1', '96.l1', '144.bl1', '144.bs1', '144.ct1'], 'contains': ['576.c1', '864.cx1', '864.df1', '864.di1', '864.dj1', '864.do1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [3096, 10368, 15552, 10924, 22752], 'label': '31104.fx.288.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1', 'old_label': '288.bj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bj1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186245618
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.h1', '96.k1', '96.l1', '144.bm1', '144.bt1', '144.ch1', '144.cu1', '144.db1'], 'contains': ['864.cy1', '864.df1', '864.dk1', '864.dl1', '864.dp1', '1152.h1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [28996, 18144, 22752, 10368, 72], 'label': '31104.fx.288.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '288.bk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bk1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
-
id: 186245619
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.b1', '96.i1', '96.l1', '96.m1', '144.bn1', '144.bu1', '144.cv1'], 'contains': ['864.cz1', '864.da1', '864.db1', '864.df1', '864.dm1', '864.dn1', '1152.i1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [76, 15552, 22752, 10368, 18648], 'label': '31104.fx.288.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1', 'old_label': '288.bl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bl1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186245620
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cy1', '96.g1', '96.k1', '96.m1', '144.bv1'], 'contains': ['576.d1', '864.dc1', '864.df1', '864.dq1', '864.dr1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [18216, 10368, 18144, 11764, 22752], 'label': '31104.fx.288.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1', 'old_label': '288.bm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bm1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 186245621
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.df1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.h1', '96.j1', '96.m1', '144.bw1', '144.dc1'], 'contains': ['864.dd1', '864.df1', '864.ds1', '864.dt1', '1152.j1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [11764, 15552, 22752, 10368, 18648], 'label': '31104.fx.288.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1', 'old_label': '288.bn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bn1', 'subgroup_fusion': None, 'weyl_group': '216.165'}
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id: 186245622
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.cz1', '96.i1', '96.j1', '96.k1', '96.m1', '144.bx1'], 'contains': ['864.de1', '864.de2', '864.df1', '864.du1', '864.dv1', '1152.k1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [29904, 15552, 22752, 10368, 18648], 'label': '31104.fx.288.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1', 'old_label': '288.bo1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bo1', 'subgroup_fusion': None, 'weyl_group': '216.165'}
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id: 186245623
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.df1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.da1', '96.g1', '144.bo1', '144.cb1', '144.cn1'], 'contains': ['576.e1', '576.f1', '864.dg1', '864.dj1', '864.dq1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [3096, 12384, 18648, 556, 12096], 'label': '31104.fx.288.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.d1', 'old_label': '288.bp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bp1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 186245624
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.df1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.h1', '144.bp1', '144.cc1', '144.ci1', '144.ci2', '144.co1', '144.dd1', '144.de1'], 'contains': ['864.dh1', '864.dl1', '864.dt1', '1152.l1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [556, 18144, 12096, 12384, 72], 'label': '31104.fx.288.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '288.bq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bq1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186245625
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '27.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['9.a1', '9.b1', '9.c1'], 'contains': ['54.q1', '54.t1', '54.w1', '54.bh1', '54.bu1', '54.bv1', '54.bw1', '81.a1', '81.c1', '108.ge1'], 'core': '108.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [5713, 15552, 22752, 2664, 24198, 5260, 2592, 18576, 36], 'label': '31104.fx.27.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '27.c1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.c1', 'subgroup_fusion': None, 'weyl_group': '1152.155790'}
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id: 186245626
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.df1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.db1', '96.g1', '144.cp1'], 'contains': ['576.g1', '576.h1', '864.dg1', '864.do1', '864.dq1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [15552, 12384, 18648, 12096, 10924], 'label': '31104.fx.288.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.q1', 'old_label': '288.br1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.br1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
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id: 186245627
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.df1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.h1', '144.cq1', '144.df1', '144.dg1'], 'contains': ['864.dh1', '864.dp1', '864.dt1', '1152.m1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [12096, 18144, 10924, 12384, 72], 'label': '31104.fx.288.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.v1', 'old_label': '288.bs1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bs1', 'subgroup_fusion': None, 'weyl_group': '72.42'}
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id: 186245628
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dc1', '96.l1', '144.cw1'], 'contains': ['864.di1', '864.dn1', '864.dp1', '864.dw1', '864.dx1', '864.ec1', '864.ed1', '864.ee1', '864.ee2', '1152.n1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [508, 18144, 5712, 12384, 72], 'label': '31104.fx.288.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.t1', 'old_label': '288.bt1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bt1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186245629
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dd1', '96.j1', '144.cd1'], 'contains': ['864.dj1', '864.ds1', '864.du1', '1152.o1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [21100, 15552, 29904, 12384, 18648], 'label': '31104.fx.288.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.l1', 'old_label': '288.bu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bu1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
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id: 186245630
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dc1', '96.l1', '144.cx1'], 'contains': ['864.dk1', '864.dm1', '864.do1', '864.dy1', '864.dz1', '864.ec1', '864.ed1', '864.ee1', '864.ee2', '1152.n1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [76, 15552, 5712, 12384, 18648], 'label': '31104.fx.288.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.t1', 'old_label': '288.bv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bv1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186245631
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.de1', '96.l1', '144.bi1', '144.ce1', '144.cy1'], 'contains': ['864.dj1', '864.dk1', '864.dm1', '864.dw1', '864.dx1', '864.ea1', '864.eb1', '1152.p1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [20812, 15552, 5712, 12384, 18648], 'label': '31104.fx.288.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1', 'old_label': '288.bw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bw1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186245632
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dd1', '96.k1', '144.cf1'], 'contains': ['864.dl1', '864.dr1', '864.dv1', '1152.o1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [21532, 18144, 29904, 12384, 72], 'label': '31104.fx.288.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.m1', 'old_label': '288.bx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bx1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
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id: 186245633
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.de1', '96.l1', '144.bj1', '144.cg1', '144.cz1'], 'contains': ['864.di1', '864.dl1', '864.dn1', '864.dy1', '864.dz1', '864.ea1', '864.eb1', '1152.p1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [21244, 18144, 5712, 12384, 72], 'label': '31104.fx.288.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1', 'old_label': '288.by1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.by1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186245636
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '27.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['9.b1', '9.d1'], 'contains': ['54.a1', '54.b1', '54.d1', '54.g1', '54.h1', '54.j1', '54.k1', '54.n1', '54.ba1', '54.bb1', '54.be1', '54.bg1', '54.bm1', '54.bp1', '54.ce1', '81.b1', '81.c1'], 'core': '648.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [5713, 22752, 72, 2592, 6, 15552, 12096, 18576, 36], 'label': '31104.fx.27.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '27.d1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.d1', 'subgroup_fusion': None, 'weyl_group': '576.7160'}
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id: 186245637
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.a1', '144.v1', '144.dh1', '144.di1', '144.dj1', '144.dk1', '144.es1'], 'contains': ['576.a1', '576.i1', '576.ca1', '864.ef1', '864.eg1', '864.eh1', '864.ei1', '864.ej1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [36, 10368, 16056, 12096, 22752], 'label': '31104.fx.288.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '288.cb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cb1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
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id: 186245638
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.gc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.w1', '144.dh1', '144.dl1', '144.dm1', '144.dn1', '144.do1', '144.dp1', '144.dq1', '144.dr1', '144.ds1', '144.dt1', '144.du1', '144.dv1', '144.eu1', '144.ev1'], 'contains': ['576.i1', '576.r1', '864.ek1', '864.el1', '864.em1', '864.en1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [12138, 10368, 16056, 12096, 22752], 'label': '31104.fx.288.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '288.cc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cc1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245639
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ep1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.x1', '144.dh1', '144.dl1', '144.dm1', '144.dn1', '144.dw1', '144.dx1', '144.dy1', '144.dz1', '144.ea1', '144.eb1', '144.ec1', '144.ed1', '144.fg1', '144.fl1'], 'contains': ['576.i1', '576.bj1', '864.eo1', '864.ep1', '864.eq1', '864.er1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [6, 22752, 16056, 10368, 12096], 'label': '31104.fx.288.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '288.cd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cd1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186245640
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.y1', '144.di1', '144.dl1', '144.do1', '144.dw1', '144.ee1', '144.ef1', '144.eg1', '144.fm1'], 'contains': ['576.i1', '576.bm1', '864.es1', '864.et1', '864.eu1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [10405, 1728, 2592, 22752, 10368], 'label': '31104.fx.288.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '288.ce1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ce1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245641
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.a1', '144.c1', '144.d1', '144.z1', '144.fq1'], 'contains': ['576.i1', '576.bz1', '576.ca1', '864.ev1', '864.ew1', '864.ew2', '864.ex1', '864.ey1', '864.ey2', '864.ez1', '864.ez2', '864.ez3'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [15588, 10368, 16056, 12096, 22752], 'label': '31104.fx.288.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1', 'old_label': '288.cf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cf1', 'subgroup_fusion': None, 'weyl_group': '54.14'}
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id: 186245642
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.d1', '144.v1', '144.dp1', '144.dx1', '144.ee1', '144.eh1', '144.fq1'], 'contains': ['576.i1', '576.bz1', '864.fa1', '864.fb1', '864.fc1', '864.fd1', '864.fe1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [18180, 10368, 16056, 12096, 22752], 'label': '31104.fx.288.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '288.cg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cg1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
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id: 186245643
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.c1', '144.ba1', '144.dm1', '144.dq1', '144.dy1', '144.ef1', '144.ei1', '144.ej1', '144.es1', '144.fq1'], 'contains': ['576.i1', '576.ca1', '864.ff1', '864.ff2', '864.fg1', '864.fg2', '864.fh1', '864.fi1', '864.fj1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [468, 10368, 16056, 12096, 22752], 'label': '31104.fx.288.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '288.ch1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ch1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
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id: 186245644
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bb1', '144.di1', '144.dr1', '144.du1', '144.dz1', '144.ec1', '144.ee1', '144.ei1', '144.ek1', '144.el1', '144.ft1'], 'contains': ['576.i1', '576.cd1', '864.fk1', '864.fl1', '864.fm1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1, 10368, 2592, 12096, 22752], 'label': '31104.fx.288.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '288.ci1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ci1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186245645
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.gc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.w1', '144.dj1', '144.dr1', '144.ds1', '144.dw1', '144.dx1', '144.dy1', '144.ea1', '144.eg1', '144.ej1', '144.ek1', '144.em1', '144.en1', '144.eu1', '144.fv1'], 'contains': ['576.i1', '864.fn1', '864.fo1', '864.fp1', '864.fv1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [2179, 22752, 12096, 10368, 18576], 'label': '31104.fx.288.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '288.cj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cj1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245646
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bc1', '144.dk1', '144.dn1', '144.dt1', '144.ea1', '144.eh1', '144.ei1', '144.em1', '144.fm1'], 'contains': ['576.i1', '864.fq1', '864.fw1', '864.fz1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [26389, 1728, 22752, 10368, 2592], 'label': '31104.fx.288.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '288.ck1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ck1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245647
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '27.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.c1', '9.d1'], 'contains': ['54.c1', '54.e1', '54.f1', '54.i1', '54.l1', '54.m1', '54.bc1', '54.bd1', '54.bk1', '54.br1', '54.by1', '81.c1'], 'core': '216.b1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [5713, 10368, 72, 2592, 24198, 15552, 22752, 18576, 36], 'label': '31104.fx.27.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '27.e1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.e1', 'subgroup_fusion': None, 'weyl_group': '576.7160'}
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id: 186245648
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ep1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.x1', '144.dj1', '144.do1', '144.dp1', '144.dq1', '144.dt1', '144.dz1', '144.eb1', '144.eg1', '144.ej1', '144.el1', '144.em1', '144.eo1', '144.fg1', '144.fw1'], 'contains': ['576.i1', '864.fr1', '864.fs1', '864.ft1', '864.fx1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [18150, 22752, 10368, 16056, 12096], 'label': '31104.fx.288.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '288.cl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cl1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186245649
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.be1', '144.dk1', '144.ds1', '144.dv1', '144.eb1', '144.ed1', '144.ef1', '144.eh1', '144.en1', '144.eo1', '144.ft1'], 'contains': ['576.i1', '864.fu1', '864.fy1', '864.ga1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [15985, 10368, 12096, 2592, 22752], 'label': '31104.fx.288.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '288.cm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cm1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186245650
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.bj1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.cr1', '96.n1', '144.ep1', '144.et1', '144.ey1', '144.fc1', '144.fj1', '144.fp1', '144.fr1'], 'contains': ['864.gc1', '864.gf1', '864.gh1', '1152.b1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [5712, 2592, 12096, 10368, 15984], 'label': '31104.fx.288.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.x1', 'old_label': '288.cn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cn1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186245651
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.cr1', '96.n1', '144.eq1', '144.ez1', '144.fd1'], 'contains': ['864.gd1', '864.gf1', '864.gh2', '1152.b1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [5188, 15984, 12096, 22752, 15624], 'label': '31104.fx.288.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.r1', 'old_label': '288.co1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.co1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186245652
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.cs1', '96.n1', '144.fe1', '144.fk1', '144.fs1'], 'contains': ['864.gc1', '864.gg1', '864.gh2', '1152.c1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [28464, 2592, 12096, 10368, 15984], 'label': '31104.fx.288.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.w1', 'old_label': '288.cp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cp1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186245653
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.cs1', '96.n1', '144.ff1'], 'contains': ['864.gd1', '864.gg1', '864.gh1', '864.gh2', '1152.c1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [28464, 432, 12096, 10368, 15624], 'label': '31104.fx.288.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.z1', 'old_label': '288.cq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cq1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
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id: 186245654
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.n1', '144.bg1', '144.es1', '144.eu1', '144.ev1', '144.fg1', '144.fl1', '144.fm1', '144.fq1', '144.ft1', '144.fv1', '144.fw1'], 'contains': ['576.i1', '864.gb1', '864.gc1', '864.gd1', '864.gi1', '864.gj1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [16056, 10368, 432, 12096, 22752], 'label': '31104.fx.288.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '288.cr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cr1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186245655
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.b1', '96.n1', '144.er1', '144.ew1', '144.fa1', '144.fb1', '144.fh1', '144.fn1', '144.fu1'], 'contains': ['864.ge1', '864.gf1', '864.gg1', '864.gi1', '864.gk1', '1152.i1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [20760, 432, 22752, 10368, 15624], 'label': '31104.fx.288.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.x1', 'old_label': '288.cs1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cs1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
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id: 186245656
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.cz1', '96.n1', '144.ex1', '144.fi1', '144.fo1'], 'contains': ['864.gh1', '864.gh2', '864.gh3', '864.gi1', '864.gl1', '1152.k1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [24268, 18576, 10368, 22752, 2664], 'label': '31104.fx.288.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.t1', 'old_label': '288.ct1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ct1', 'subgroup_fusion': None, 'weyl_group': '144.189'}
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id: 186245657
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.g1', '96.o1', '144.fx1'], 'contains': ['576.j1', '576.q1', '576.bg1', '864.gm1', '864.go1', '864.gq1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [29503, 10368, 36, 18672, 25852], 'label': '31104.fx.288.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fx1', 'old_label': '288.cu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cu1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245658
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '32.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '16.a1', '16.b1', '16.c1'], 'contains': ['96.g1', '96.h1', '96.i1', '96.j1', '96.k1', '96.l1', '96.m1', '128.a1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [76, 18648, 10368, 5712, 15552, 12096, 22752], 'label': '31104.fx.32.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1', 'old_label': '32.a1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.a1', 'subgroup_fusion': None, 'weyl_group': '432.747'}
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id: 186245659
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.h1', '96.o1', '144.fx1'], 'contains': ['576.j1', '576.v1', '576.z1', '864.gm1', '864.gp1', '864.gr1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [19135, 22752, 36, 18672, 15484], 'label': '31104.fx.288.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fx1', 'old_label': '288.cv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cv1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245660
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.bg1', '96.p1', '144.fx1'], 'contains': ['576.j1', '576.bs1', '576.ch1', '864.gn1', '864.gs1', '864.gt1', '864.gu1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [1, 10368, 36, 10228, 16080], 'label': '31104.fx.288.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fx1', 'old_label': '288.cw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cw1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
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id: 186245661
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bh1', '72.bi1', '96.p1'], 'contains': ['576.k1', '576.bw1', '576.cl1', '864.gn1', '864.gv1', '864.gw1', '864.gx1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [20737, 12384, 36, 18580, 16080], 'label': '31104.fx.288.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.cx1', 'old_label': '288.cx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cx1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
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id: 186245662
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ea1', '96.q1', '144.fy1'], 'contains': ['576.l1', '576.p1', '576.bc1', '864.go1', '864.gy1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [26047, 10368, 36, 5712, 12096], 'label': '31104.fx.288.cy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fy1', 'old_label': '288.cy1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cy1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
-
id: 186245663
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.eb1', '96.o1', '96.q1', '144.fz1'], 'contains': ['576.n1', '576.s1', '576.ba1', '864.go1', '864.gp1', '864.ha1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [19135, 10368, 36, 5712, 22752], 'label': '31104.fx.288.cz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fz1', 'old_label': '288.cz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cz1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 186245664
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ec1', '72.ed1', '96.r1', '144.fy1'], 'contains': ['576.l1', '576.u1', '576.bb1', '864.gr1', '864.gz1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [26047, 22752, 36, 23836, 12096], 'label': '31104.fx.288.da1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fy1', 'old_label': '288.da1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.da1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
-
id: 186245665
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ee1', '96.o1', '96.r1', '144.fz1'], 'contains': ['576.n1', '576.x1', '576.bk1', '864.gq1', '864.gr1', '864.ha1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [19135, 10368, 36, 25852, 22752], 'label': '31104.fx.288.db1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bc1', 'old_label': '288.db1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.db1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
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id: 186245666
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bk1', '96.p1', '96.s1', '144.f1'], 'contains': ['576.m1', '576.bn1', '576.ci1', '864.gs1', '864.gv1', '864.gw1', '864.hb1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [1, 10368, 36, 10924, 2016], 'label': '31104.fx.288.dc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.f1', 'old_label': '288.dc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dc1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
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id: 186245667
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.bl1', '72.ef1', '96.p1', '96.t1', '144.fz1'], 'contains': ['576.n1', '576.bo1', '576.cj1', '864.gt1', '864.gu1', '864.gx1', '864.hb1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [1, 10368, 36, 5712, 22752], 'label': '31104.fx.288.dd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fz1', 'old_label': '288.dd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dd1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
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id: 186245668
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.bm1', '72.eg1', '96.t1', '144.fy1'], 'contains': ['576.l1', '576.br1', '576.cb1', '864.gu1', '864.hc1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [1, 10368, 36, 5712, 12096], 'label': '31104.fx.288.de1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fy1', 'old_label': '288.de1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.de1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
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id: 186245669
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '4.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': ['7776.y1', '7776.bb1', '7776.ba1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '2.d1', '2.e1'], 'contains': ['8.a1', '12.e1', '12.v1', '12.w1', '16.c1'], 'core': '4.e1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 18144, 22752, 10368, 15552, 12096, 5712, 15984, 15624, 76], 'label': '31104.fx.4.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': ['2.b1', '2.d1', '2.e1'], 'normal_contains': ['8.a1', '12.e1'], 'normalizer': '1.a1', 'old_label': '4.e1', 'projective_image': '31104.fx', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.e1', 'subgroup_fusion': None, 'weyl_group': '31104.fx'}
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id: 186245670
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '32.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '16.d1'], 'contains': ['64.a1', '64.b1', '64.c1', '96.o1', '96.q1', '96.r1'], 'core': '576.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [26047, 10368, 12096, 36, 22752, 8304, 3100], 'label': '31104.fx.32.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.d1', 'old_label': '32.b1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.b1', 'subgroup_fusion': None, 'weyl_group': '1944.2342'}
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id: 186245671
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bo1', '96.s1', '144.g1'], 'contains': ['576.o1', '576.bu1', '576.ce1', '864.gw1', '864.hd1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [20737, 12384, 36, 556, 1728], 'label': '31104.fx.288.df1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.g1', 'old_label': '288.df1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.df1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
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id: 186245672
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.q1', '96.r1', '144.dh1', '144.ga1'], 'contains': ['576.a1', '576.r1', '576.bj1', '864.gy1', '864.gz1', '864.ha1'], 'core': '576.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [6, 22752, 36, 12096, 10368], 'label': '31104.fx.288.dg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.x1', 'old_label': '288.dg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dg1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
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id: 186245673
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.s1', '96.t1', '144.j1', '144.di1', '144.ga1'], 'contains': ['576.a1', '576.bm1', '576.cd1', '864.hb1', '864.hc1', '864.hd1'], 'core': '576.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1, 10368, 36, 12096, 22752], 'label': '31104.fx.288.dh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.c1', 'old_label': '288.dh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dh1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
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id: 186245674
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.el1', '96.u1', '144.fy1'], 'contains': ['576.p1', '576.bb1', '576.br1', '864.he1', '864.hf1', '864.hg1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [10405, 10368, 6, 28176, 1728], 'label': '31104.fx.288.di1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fy1', 'old_label': '288.di1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.di1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186245675
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.v1', '96.w1', '144.fx1'], 'contains': ['576.q1', '576.z1', '576.bs1', '864.hf1', '864.hi1', '864.hk1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [10405, 16080, 12138, 22752, 30964], 'label': '31104.fx.288.dj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fx1', 'old_label': '288.dj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dj1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245676
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.u1', '96.v1', '144.dl1', '144.ga1', '144.gb1'], 'contains': ['576.r1', '576.bj1', '576.bm1', '864.he1', '864.hj1', '864.hn1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [26485, 22752, 6, 10368, 12096], 'label': '31104.fx.288.dk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.di1', 'old_label': '288.dk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dk1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245677
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.er1', '96.u1', '96.w1', '144.fz1'], 'contains': ['576.s1', '576.bk1', '576.bo1', '864.hf1', '864.hj1', '864.ho1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [26485, 10368, 30714, 22752, 28012], 'label': '31104.fx.288.dl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fz1', 'old_label': '288.dl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dl1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245678
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.es1', '96.u1', '96.x1'], 'contains': ['576.t1', '576.bl1', '576.bq1', '864.hg1', '864.hj1', '864.hp1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 576, 'diagramx': None, 'generators': [26485, 10368, 30714, 22752, 29452], 'label': '31104.fx.288.dm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.dm1', 'old_label': '288.dm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dm1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186245679
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dh1', '144.dm1', '144.gb1'], 'contains': ['576.r1', '576.bj1', '576.ca1', '864.hh1', '864.hl1', '864.hl2', '864.hm1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [26047, 10368, 18612, 12096, 22752], 'label': '31104.fx.288.dn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.dl1', 'old_label': '288.dn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dn1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
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id: 186245680
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.y1', '144.du1', '144.ga1', '144.gb1'], 'contains': ['576.r1', '576.cd1', '864.hq1', '864.hs1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [5713, 10368, 12138, 12096, 22752], 'label': '31104.fx.288.do1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.di1', 'old_label': '288.do1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.do1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245681
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '32.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1', '16.d1'], 'contains': ['64.a1', '64.d1', '64.e1', '96.p1', '96.s1', '96.t1'], 'core': '576.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [1, 22752, 12096, 36, 10368, 18580, 5712], 'label': '31104.fx.32.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.d1', 'old_label': '32.c1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.c1', 'subgroup_fusion': None, 'weyl_group': '1944.2342'}
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id: 186245682
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.eu1', '96.v1', '96.w1', '96.x1', '144.fz1'], 'contains': ['576.x1', '576.ba1', '576.bo1', '864.hi1', '864.hj1', '864.hv1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [7477, 22752, 18582, 10368, 5260], 'label': '31104.fx.288.dp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fz1', 'old_label': '288.dp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dp1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245683
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ev1', '96.v1', '144.fy1'], 'contains': ['576.u1', '576.bc1', '576.br1', '864.hn1', '864.hv1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [26485, 22752, 18582, 28012, 12096], 'label': '31104.fx.288.dq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bd1', 'old_label': '288.dq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dq1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
-
id: 186245684
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.bc1', '96.w1', '144.fx1'], 'contains': ['576.v1', '576.bg1', '576.bs1', '864.hk1', '864.ho1', '864.hv1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [10405, 10368, 12138, 30964, 16080], 'label': '31104.fx.288.dr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bc1', 'old_label': '288.dr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dr1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
-
id: 186245685
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.bd1', '96.x1'], 'contains': ['576.w1', '576.bh1', '576.bt1', '864.hp1', '864.hv1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [10405, 10368, 12138, 6484, 16080], 'label': '31104.fx.288.ds1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.x1', 'old_label': '288.ds1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ds1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
-
id: 186245686
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ex1', '96.y1', '144.fy1'], 'contains': ['576.p1', '576.u1', '576.cb1', '864.hq1', '864.hw1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [5713, 22752, 30714, 12096, 5260], 'label': '31104.fx.288.dt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fy1', 'old_label': '288.dt1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dt1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
-
id: 186245687
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.bf1', '96.z1', '144.fx1'], 'contains': ['576.q1', '576.v1', '576.ch1', '864.hr1', '864.ht1', '864.hu1', '864.hw1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [1, 10368, 12138, 18580, 5712], 'label': '31104.fx.288.du1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fx1', 'old_label': '288.du1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.du1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
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id: 186245688
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.dv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ey1', '96.y1', '96.z1', '144.fz1'], 'contains': ['576.s1', '576.x1', '576.cj1', '864.hr1', '864.hs1', '864.hw1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [1, 10368, 12138, 5712, 22752], 'label': '31104.fx.288.dv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bd1', 'old_label': '288.dv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dv1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
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id: 186245689
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.bh1', '96.ba1'], 'contains': ['576.y1', '576.bf1', '576.cg1', '864.hy1', '864.ib1', '864.ic1', '864.id1', '864.ie1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 576, 'diagramx': None, 'generators': [1, 10368, 22758, 18580, 28464], 'label': '31104.fx.288.dw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.dw1', 'old_label': '288.dw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dw1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
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id: 186245690
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.dx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.bi1', '96.ba1', '144.fx1'], 'contains': ['576.z1', '576.bg1', '576.ch1', '864.hx1', '864.ia1', '864.ic1', '864.ie1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [1, 22752, 6, 8212, 5712], 'label': '31104.fx.288.dx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fx1', 'old_label': '288.dx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dx1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
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id: 186245691
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.fb1', '96.ba1', '96.bb1', '144.fz1'], 'contains': ['576.ba1', '576.bk1', '576.cj1', '864.hx1', '864.hy1', '864.hz1', '864.ie1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [5713, 10368, 18582, 15628, 22752], 'label': '31104.fx.288.dy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fz1', 'old_label': '288.dy1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dy1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
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id: 186245692
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.c1', '16.d1'], 'contains': ['64.b1', '64.c1', '64.d1', '96.u1', '96.v1', '96.w1', '96.x1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [10405, 22752, 1728, 12138, 10368, 30964, 16080], 'label': '31104.fx.32.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.d1', 'old_label': '32.d1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
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id: 186245693
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.fd1', '96.bb1', '144.fy1'], 'contains': ['576.bb1', '576.bc1', '576.cb1', '864.hx1', '864.if1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [1, 10368, 6, 5712, 12096], 'label': '31104.fx.288.dz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fy1', 'old_label': '288.dz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dz1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
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id: 186245695
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.eb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bb1', '144.ec1', '144.ga1', '144.gb1'], 'contains': ['576.bj1', '576.cd1', '864.hz1', '864.if1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [5713, 10368, 6, 12096, 22752], 'label': '31104.fx.288.eb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.di1', 'old_label': '288.eb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.eb1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
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id: 186245696
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.ec1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bq1', '96.bc1', '144.f1'], 'contains': ['576.bn1', '576.bx1', '576.ci1', '864.ig1', '864.ii1', '864.ij1', '864.ik1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [1, 10368, 15588, 10924, 2016], 'label': '31104.fx.288.ec1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.f1', 'old_label': '288.ec1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ec1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
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id: 186245697
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.ed1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bc1', '144.j1', '144.m1', '144.ee1'], 'contains': ['576.bm1', '576.bz1', '576.cd1', '864.ig1', '864.il1', '864.im1', '864.im2'], 'core': '1152.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [1, 10368, 18180, 12096, 22752], 'label': '31104.fx.288.ed1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.f1', 'old_label': '288.ed1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ed1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
-
id: 186245698
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.ee1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.m1', '144.di1', '144.gb1'], 'contains': ['576.bm1', '576.ca1', '576.cd1', '864.ih1', '864.in1', '864.io1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1, 10368, 2628, 12096, 22752], 'label': '31104.fx.288.ee1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.c1', 'old_label': '288.ee1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ee1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
-
id: 186245699
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '288.ef1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bs1', '96.bc1', '144.g1'], 'contains': ['576.bu1', '576.by1', '576.ce1', '864.ik1', '864.im1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [20737, 12384, 15588, 556, 1728], 'label': '31104.fx.288.ef1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.g1', 'old_label': '288.ef1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ef1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
-
id: 186245700
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.s1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.b1', '162.c1'], 'contains': ['648.k1', '648.p1', '648.z1', '648.be1', '648.bn1', '648.ge1', '648.gh1', '648.go1', '648.gt1', '648.hf1', '648.ib1', '972.a1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [5713, 12096, 18576, 6, 36, 18648], 'label': '31104.fx.324.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '324.a1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 186245701
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.w1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.c1', '162.c1'], 'contains': ['648.k1', '648.v1', '648.bd1', '648.bf1', '648.bo1', '648.gg1', '648.gi1', '648.gq1', '648.gu1', '648.hg1', '648.ic1', '972.b1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [8305, 12096, 18576, 6, 36, 18648], 'label': '31104.fx.324.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '324.b1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.b1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 186245702
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.b1', '108.d1', '162.e1'], 'contains': ['648.j1', '648.m1', '648.n1', '648.x1', '648.bh1', '648.bj1', '648.bl1', '648.gd1', '648.gj1', '648.gl1', '648.gn1', '648.gr1', '648.hh1', '648.hr1', '648.hz1', '972.a1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 22752, 18576, 24198, 36, 18648], 'label': '31104.fx.324.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '324.c1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.c1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 186245703
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '32.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1', '16.d1'], 'contains': ['64.b1', '64.e1', '96.y1', '96.z1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [1, 22752, 5712, 12138, 10368, 12096, 18580], 'label': '31104.fx.32.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.d1', 'old_label': '32.e1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.e1', 'subgroup_fusion': None, 'weyl_group': '1944.2342'}
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id: 186245704
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.u1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.c1', '108.e1', '162.e1'], 'contains': ['648.j1', '648.m1', '648.q1', '648.y1', '648.bi1', '648.bk1', '648.bm1', '648.gf1', '648.gk1', '648.gm1', '648.gp1', '648.gs1', '648.hi1', '648.hs1', '648.ia1', '972.b1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [8305, 10368, 18576, 24198, 36, 18648], 'label': '31104.fx.324.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '324.d1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.d1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 186245705
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.f1', '162.c1'], 'contains': ['648.z1', '648.bb1', '648.bf1', '648.bo1', '648.bu1', '648.gx1', '648.ha1', '648.hd1', '648.hw1', '972.c1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [8305, 12096, 18576, 6, 2628, 18648], 'label': '31104.fx.324.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '324.e1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.e1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
-
id: 186245706
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.g1', '162.c1'], 'contains': ['648.bb1', '648.bd1', '648.be1', '648.bn1', '648.cg1', '648.gy1', '648.hb1', '648.he1', '648.hx1', '972.d1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [5713, 12096, 18576, 6, 2628, 18648], 'label': '31104.fx.324.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '324.f1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.f1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
-
id: 186245707
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.f1', '108.h1', '162.e1'], 'contains': ['648.x1', '648.ba1', '648.bg1', '648.bh1', '648.bk1', '648.bm1', '648.br1', '648.gv1', '648.gz1', '648.hj1', '648.hl1', '648.hn1', '648.hp1', '648.ht1', '648.hv1', '972.c1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [8305, 10368, 18576, 24198, 2628, 18648], 'label': '31104.fx.324.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '324.g1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.g1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
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id: 186245708
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.g1', '108.i1', '162.e1'], 'contains': ['648.y1', '648.ba1', '648.bg1', '648.bi1', '648.bj1', '648.bl1', '648.ch1', '648.gw1', '648.hc1', '648.hk1', '648.hm1', '648.ho1', '648.hq1', '648.hu1', '648.hy1', '972.d1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 22752, 18576, 24198, 2628, 18648], 'label': '31104.fx.324.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '324.h1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.h1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
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id: 186245709
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.j1', '108.m1', '162.a1', '162.e1', '162.s1'], 'contains': ['648.j1', '648.ba1', '648.cn1', '648.cs1', '648.cx1', '648.ig1', '648.ij1', '648.iq1', '648.iv1', '648.jh1', '648.ke1', '972.e1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [29503, 10368, 18576, 36, 16056, 2592], 'label': '31104.fx.324.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '324.i1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.i1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186245710
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.j1', '108.l1', '162.b1', '162.c1', '162.t1'], 'contains': ['648.k1', '648.bb1', '648.cp1', '648.ct1', '648.cy1', '648.ih1', '648.ik1', '648.is1', '648.iw1', '648.ji2', '648.kf1', '972.e1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [6, 12096, 18576, 36, 16056, 2592], 'label': '31104.fx.324.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '324.j1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.j1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186245711
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.j1', '108.k1', '162.t1'], 'contains': ['648.l1', '648.bc1', '648.cq1', '648.cu1', '648.cz1', '648.ii1', '648.ik1', '648.it1', '648.ix1', '648.ji1', '648.kg1', '972.e1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [26047, 12096, 2592, 36, 15552, 18576], 'label': '31104.fx.324.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.t1', 'old_label': '324.k1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.k1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245712
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.k1', '108.l1', '108.m1', '162.d1', '162.e1', '162.u1'], 'contains': ['648.m1', '648.bg1', '648.cn1', '648.cv1', '648.cw1', '648.il1', '648.im1', '648.ir1', '648.jj1', '648.js1', '648.jw1', '972.e1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [19135, 22752, 18576, 36, 16056, 2592], 'label': '31104.fx.324.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '324.l1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.l1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186245713
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.n1', '108.o1', '162.e1', '162.f1', '162.v1'], 'contains': ['648.n1', '648.q1', '648.br1', '648.ch1', '648.cn1', '648.da1', '648.dj1', '648.in1', '648.in2', '648.kj1', '648.kj2', '972.f1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [20737, 22752, 2592, 36, 18576, 15552], 'label': '31104.fx.324.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '324.m1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.m1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186245714
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '32.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1', '16.d1'], 'contains': ['64.c1', '64.e1', '96.ba1', '96.bb1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [1, 22752, 12096, 6, 10368, 18580, 5712], 'label': '31104.fx.32.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.d1', 'old_label': '32.f1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.f1', 'subgroup_fusion': None, 'weyl_group': '1944.2342'}
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id: 186245715
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.n1', '108.p1', '162.w1'], 'contains': ['648.o1', '648.s1', '648.bs1', '648.ci1', '648.co1', '648.db1', '648.dk1', '648.io1', '648.kk1', '972.f1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [20737, 12384, 2592, 36, 18576, 15552], 'label': '31104.fx.324.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.w1', 'old_label': '324.n1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.n1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245716
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.o1', '108.p1', '162.c1', '162.g1', '162.x1'], 'contains': ['648.p1', '648.v1', '648.bu1', '648.cg1', '648.cp1', '648.dc1', '648.di1', '648.ip1', '648.kl1', '972.f1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [20737, 1728, 2592, 36, 18576, 15552], 'label': '31104.fx.324.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '324.o1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.o1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
-
id: 186245717
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.q1', '108.u1', '162.d1', '162.f1', '162.s1'], 'contains': ['648.cn1', '648.dl1', '648.dp1', '648.iq1', '648.km1', '972.g1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [13951, 10368, 18576, 36, 16056, 2592], 'label': '31104.fx.324.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '324.p1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.p1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
-
id: 186245718
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.r1', '108.s1', '108.u1', '162.a1', '162.f1', '162.u1'], 'contains': ['648.cn1', '648.dm1', '648.do1', '648.ir1', '648.kn1', '972.g1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [3583, 22752, 18576, 36, 16056, 2592], 'label': '31104.fx.324.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '324.q1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.q1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186245719
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.t1', '108.v1', '162.a1', '162.d1', '162.v1'], 'contains': ['648.r1', '648.cj1', '648.cn1', '648.dn1', '648.dq1', '972.h1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [16057, 10368, 2592, 36, 18576, 15552], 'label': '31104.fx.324.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '324.r1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.r1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186245720
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.v1', '108.w1', '162.w1'], 'contains': ['648.t1', '648.u1', '648.ck1', '648.cl1', '648.co1', '648.dr1', '648.ds1', '972.h1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [5689, 12384, 15552, 36, 18576, 2592], 'label': '31104.fx.324.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.w1', 'old_label': '324.s1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.s1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245721
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.q1', '108.s1', '162.b1', '162.g1', '162.t1'], 'contains': ['648.cp1', '648.dt1', '648.dw1', '648.it1', '648.kp2', '972.g1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [15558, 12096, 18576, 36, 2592, 2664], 'label': '31104.fx.324.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '324.t1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.t1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
-
id: 186245722
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.q1', '108.r1', '162.t1'], 'contains': ['648.cq1', '648.du1', '648.dx1', '648.is1', '648.it1', '648.ko1', '648.kp1', '972.g1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [25975, 12096, 18576, 36, 15552, 2592], 'label': '31104.fx.324.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.t1', 'old_label': '324.u1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.u1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245723
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.t1', '108.w1', '162.b1', '162.x1'], 'contains': ['648.w1', '648.cm1', '648.cp1', '648.dv1', '648.dy1', '972.h1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [5689, 1728, 2592, 36, 18576, 15552], 'label': '31104.fx.324.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '324.v1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.v1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
-
id: 186245724
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.x1', '108.bb1', '162.e1', '162.h1', '162.y1'], 'contains': ['648.x1', '648.y1', '648.cs1', '648.cw1', '648.da1', '648.iu1', '648.iz1', '648.jd1', '648.ju1', '972.i1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [7477, 18576, 10368, 6, 16056, 2592], 'label': '31104.fx.324.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '324.w1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.w1', 'subgroup_fusion': None, 'weyl_group': '64.202'}
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id: 186245725
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': ['864.ic1', '864.ib1', '864.id1', '864.ia1', '864.hk1', '864.ht1', '864.hu1'], 'conjugacy_class_count': 1, 'contained_in': ['12.a1', '12.k1', '18.s1', '18.t1'], 'contains': ['72.a1', '72.w1', '72.ba1', '72.bw1', '72.ce1', '108.du1', '108.dv1', '108.dw1'], 'core': '36.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [36, 15552, 12096, 16056, 18144, 10368, 22752, 18576], 'label': '31104.fx.36.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': ['12.a1'], 'normal_contains': ['72.a1', '576.a1'], 'normalizer': '1.a1', 'old_label': '36.a1', 'projective_image': '31104.fx', 'quotient_action_image': '36.10', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '36.a1', 'subgroup_fusion': None, 'weyl_group': '1944.2342'}
-
id: 186245726
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.x1', '108.bc1', '162.c1', '162.i1', '162.z1'], 'contains': ['648.z1', '648.bd1', '648.ct1', '648.cy1', '648.dc1', '648.iy1', '648.ja1', '648.je1', '648.jy1', '972.i1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [26485, 12096, 18576, 6, 16056, 2592], 'label': '31104.fx.324.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '324.x1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.x1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
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id: 186245727
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.y1', '108.bf1', '162.h1', '162.l1', '162.s1'], 'contains': ['648.cs1', '648.dd1', '648.dp1', '648.jh1', '648.km1', '972.j1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [13951, 10368, 18576, 15588, 16056, 2592], 'label': '31104.fx.324.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '324.y1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.y1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186245728
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.y1', '108.be1', '162.i1', '162.j1', '162.t1'], 'contains': ['648.ct1', '648.df1', '648.dw1', '648.ji1', '648.ko1', '972.j1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [15558, 12096, 18576, 15588, 2592, 2664], 'label': '31104.fx.324.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '324.z1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.z1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186245729
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.y1', '108.bd1', '162.t1'], 'contains': ['648.cu1', '648.dg1', '648.dx1', '648.ji1', '648.ji2', '648.kp1', '648.kp2', '972.j1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [2598, 12096, 18576, 2628, 18144, 16056], 'label': '31104.fx.324.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.t1', 'old_label': '324.ba1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.ba1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245730
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.z1', '108.bi1', '162.a1', '162.l1', '162.y1'], 'contains': ['648.cs1', '648.dn1', '648.do1', '972.k1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [23029, 18576, 15984, 15558, 10368, 18648], 'label': '31104.fx.324.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '324.bb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bb1', 'subgroup_fusion': None, 'weyl_group': '64.202'}
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id: 186245731
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.ba1', '108.bj1', '162.a1', '162.h1', '162.bf1'], 'contains': ['648.cs1', '648.dm1', '648.dq1', '972.l1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [21265, 10368, 18576, 27690, 18648, 15984], 'label': '31104.fx.324.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '324.bc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bc1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
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id: 186245732
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.z1', '108.bg1', '162.b1', '162.j1', '162.z1'], 'contains': ['648.ct1', '648.dv1', '648.dw1', '972.k1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [10933, 12096, 18576, 12138, 18648, 15984], 'label': '31104.fx.324.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '324.bd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bd1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
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id: 186245733
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.ba1', '108.bh1', '162.b1', '162.i1', '162.bc1'], 'contains': ['648.ct1', '648.dt1', '648.dy1', '972.l1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [21265, 18576, 15984, 27690, 12096, 18648], 'label': '31104.fx.324.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '324.be1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.be1', 'subgroup_fusion': None, 'weyl_group': '64.202'}
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id: 186245734
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.bk1', '162.c1', '162.j1', '162.bc1'], 'contains': ['648.be1', '648.bf1', '648.ct1', '648.di1', '648.jb1', '648.jn1', '972.m1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [5713, 18576, 12096, 12138, 16056, 2592], 'label': '31104.fx.324.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '324.bf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bf1', 'subgroup_fusion': None, 'weyl_group': '64.202'}
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id: 186245735
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.bb1', '108.bc1', '162.e1', '162.k1', '162.be1'], 'contains': ['648.bh1', '648.bi1', '648.cv1', '648.cx1', '648.da1', '648.jl1', '648.jm1', '648.jr1', '648.jx1', '972.i1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [26485, 10368, 18576, 12138, 16056, 2592], 'label': '31104.fx.324.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '324.bg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bg1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
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id: 186245736
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['12.b1', '12.c1', '12.m1', '18.n1', '18.ba1', '18.bg1'], 'contains': ['72.b1', '108.a1', '108.eb1', '108.ee1', '144.fa1'], 'core': '36.b1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [17371, 16056, 18576, 10368, 22752, 15552, 2592, 23836], 'label': '31104.fx.36.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.b1', 'normal_contained_in': ['12.b1', '12.c1'], 'normal_contains': ['72.b1', '108.a1'], 'normalizer': '1.a1', 'old_label': '36.b1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.b1', 'subgroup_fusion': None, 'weyl_group': '10368.pi'}
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id: 186245737
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.bd1', '108.be1', '108.bf1', '162.k1', '162.l1', '162.u1'], 'contains': ['648.cv1', '648.dd1', '648.do1', '648.js1', '648.kn1', '972.j1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [3583, 22752, 18576, 15588, 16056, 2592], 'label': '31104.fx.324.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '324.bh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bh1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186245738
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.bg1', '108.bi1', '162.d1', '162.l1', '162.be1'], 'contains': ['648.cv1', '648.dn1', '648.dp1', '972.k1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [10933, 10368, 18576, 12138, 18648, 15984], 'label': '31104.fx.324.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '324.bi1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bi1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
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id: 186245739
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.bh1', '108.bj1', '162.d1', '162.k1', '162.bf1'], 'contains': ['648.cv1', '648.dl1', '648.dq1', '972.l1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [21265, 10368, 18576, 12138, 18648, 15984], 'label': '31104.fx.324.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '324.bj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bj1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
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id: 186245740
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.bk1', '108.bl1', '162.e1', '162.l1', '162.bf1'], 'contains': ['648.bj1', '648.bk1', '648.cs1', '648.cv1', '648.dj1', '648.jc1', '648.jo1', '648.jp1', '648.jt1', '972.m1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [5713, 22752, 18576, 12138, 16056, 2592], 'label': '31104.fx.324.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '324.bk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bk1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
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id: 186245741
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.bm1', '108.bn1', '108.bo1', '162.h1', '162.m1', '162.u1'], 'contains': ['648.cw1', '648.dd1', '648.dm1', '648.jw1', '648.kn1', '972.n1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [19135, 22752, 18576, 15588, 16056, 2592], 'label': '31104.fx.324.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '324.bl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bl1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186245742
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.bp1', '108.br1', '162.d1', '162.m1', '162.y1'], 'contains': ['648.cw1', '648.dl1', '648.dn1', '972.o1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [23029, 18576, 15984, 6, 10368, 18648], 'label': '31104.fx.324.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '324.bm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bm1', 'subgroup_fusion': None, 'weyl_group': '64.202'}
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id: 186245743
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.bq1', '108.bs1', '162.d1', '162.h1', '162.bh1'], 'contains': ['648.cw1', '648.dp1', '648.dq1', '972.p1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [21265, 22752, 18576, 15558, 18648, 15984], 'label': '31104.fx.324.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '324.bn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bn1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
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id: 186245744
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.bo1', '108.bu1', '162.k1', '162.m1', '162.s1'], 'contains': ['648.cx1', '648.dd1', '648.dl1', '648.ke1', '648.km1', '972.n1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [29503, 10368, 18576, 15588, 16056, 2592], 'label': '31104.fx.324.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '324.bo1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bo1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186245745
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.bn1', '108.bu1', '162.i1', '162.n1', '162.t1'], 'contains': ['648.cy1', '648.df1', '648.dt1', '648.kg1', '648.kp1', '972.n1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [6, 12096, 18576, 15588, 2592, 2664], 'label': '31104.fx.324.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '324.bp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bp1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
-
id: 186245746
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.bm1', '108.bu1', '162.t1'], 'contains': ['648.cz1', '648.dg1', '648.du1', '648.kf1', '648.kg1', '648.ko1', '648.kp2', '972.n1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [6, 12096, 18576, 2628, 18144, 16056], 'label': '31104.fx.324.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.t1', 'old_label': '324.bq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bq1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245747
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1'], 'contains': ['72.e1', '72.f1', '72.i1', '72.l1', '72.n1', '72.dg1', '72.di1', '72.dk1', '72.dm1', '72.du1', '72.dy1', '108.b1', '108.d1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [5713, 18576, 12096, 6, 18648, 10368, 22752, 36], 'label': '31104.fx.36.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '36.c1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
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id: 186245748
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.br1', '108.bv1', '162.a1', '162.m1', '162.be1'], 'contains': ['648.cx1', '648.dm1', '648.dn1', '972.o1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [10933, 10368, 18576, 27690, 18648, 15984], 'label': '31104.fx.324.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '324.br1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.br1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
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id: 186245749
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.bs1', '108.bw1', '162.a1', '162.k1', '162.bh1'], 'contains': ['648.cx1', '648.do1', '648.dq1', '972.p1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [21265, 22752, 18576, 6, 18648, 15984], 'label': '31104.fx.324.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '324.bs1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bs1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
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id: 186245750
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.bp1', '108.bv1', '162.b1', '162.n1', '162.z1'], 'contains': ['648.cy1', '648.dt1', '648.dv1', '972.o1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [10933, 12096, 18576, 6, 18648, 15984], 'label': '31104.fx.324.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '324.bt1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bt1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
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id: 186245751
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.bq1', '108.bw1', '162.b1', '162.i1', '162.bk1'], 'contains': ['648.cy1', '648.dw1', '648.dy1', '972.p1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [21265, 12096, 18576, 15558, 18648, 15984], 'label': '31104.fx.324.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '324.bu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bu1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
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id: 186245752
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.bt1', '108.bx1', '162.e1', '162.m1', '162.bh1'], 'contains': ['648.bl1', '648.bm1', '648.cw1', '648.cx1', '648.dj1', '648.jv1', '648.ka1', '648.kb1', '648.kh1', '972.q1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [5713, 22752, 18576, 6, 16056, 2592], 'label': '31104.fx.324.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '324.bv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bv1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
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id: 186245753
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.bx1', '162.c1', '162.n1', '162.bk1'], 'contains': ['648.bn1', '648.bo1', '648.cy1', '648.di1', '648.jz1', '648.ki1', '972.q1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [5713, 12096, 18576, 6, 16056, 2592], 'label': '31104.fx.324.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '324.bw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bw1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
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id: 186245754
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.by1', '108.ca1', '162.h1', '162.k1', '162.v1'], 'contains': ['648.bp1', '648.bz1', '648.da1', '648.dd1', '648.dq1', '972.r1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [16057, 10368, 2592, 16092, 18576, 15552], 'label': '31104.fx.324.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '324.bx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bx1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186245755
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.by1', '108.cb1', '162.w1'], 'contains': ['648.bq1', '648.bq2', '648.cb1', '648.cb2', '648.db1', '648.de1', '648.ds1', '972.r1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [5689, 12384, 15552, 16092, 18576, 2592], 'label': '31104.fx.324.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.w1', 'old_label': '324.by1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.by1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245756
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.bz1', '108.cc1', '162.f1', '162.k1', '162.y1'], 'contains': ['648.da1', '648.dl1', '648.do1', '972.s1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [7477, 18576, 15984, 15558, 10368, 18648], 'label': '31104.fx.324.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '324.bz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bz1', 'subgroup_fusion': None, 'weyl_group': '64.202'}
-
id: 186245757
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.bz1', '108.cd1', '162.f1', '162.h1', '162.be1'], 'contains': ['648.da1', '648.dm1', '648.dp1', '972.s1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [26485, 10368, 18576, 27690, 18648, 15984], 'label': '31104.fx.324.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '324.ca1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.ca1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
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id: 186245758
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1'], 'contains': ['72.e1', '72.g1', '72.k1', '72.m1', '72.o1', '72.dh1', '72.dj1', '72.dl1', '72.dn1', '72.dv1', '72.dz1', '108.c1', '108.e1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [8305, 18576, 12096, 6, 18648, 10368, 22752, 36], 'label': '31104.fx.36.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '36.d1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.d1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
-
id: 186245759
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.ca1', '108.cb1', '162.i1', '162.x1'], 'contains': ['648.bt1', '648.ce1', '648.dc1', '648.df1', '648.dy1', '972.r1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [5689, 1728, 2592, 16092, 18576, 15552], 'label': '31104.fx.324.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '324.cb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.cb1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186245760
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.cc1', '108.cd1', '162.g1', '162.i1', '162.z1'], 'contains': ['648.dc1', '648.dt1', '648.dw1', '972.s1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [26485, 12096, 18576, 27690, 18648, 15984], 'label': '31104.fx.324.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '324.cc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.cc1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
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id: 186245761
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.ce1', '108.cf1', '162.j1', '162.n1', '162.x1'], 'contains': ['648.bv1', '648.cf1', '648.df1', '648.di1', '648.dv1', '972.t1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [20737, 1728, 2592, 16092, 18576, 15552], 'label': '31104.fx.324.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '324.cd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.cd1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186245762
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.ce1', '108.cg1', '162.l1', '162.m1', '162.v1'], 'contains': ['648.bw1', '648.ca1', '648.dd1', '648.dj1', '648.dn1', '972.t1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1, 10368, 2592, 16092, 18576, 15552], 'label': '31104.fx.324.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '324.ce1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.ce1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186245763
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.cf1', '108.cg1', '162.w1'], 'contains': ['648.bx1', '648.by1', '648.cc1', '648.cd1', '648.de1', '648.dk1', '648.dr1', '972.t1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [20737, 12384, 15552, 16092, 18576, 2592], 'label': '31104.fx.324.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.w1', 'old_label': '324.cf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.cf1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 186245764
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.ch1', '162.g1', '162.n1', '162.bc1'], 'contains': ['648.di1', '648.dt1', '972.u1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [5713, 18576, 15984, 27690, 12096, 18648], 'label': '31104.fx.324.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '324.cg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.cg1', 'subgroup_fusion': None, 'weyl_group': '64.202'}
-
id: 186245765
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.ci1', '162.g1', '162.j1', '162.bk1'], 'contains': ['648.di1', '648.dw1', '972.v1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [5713, 12096, 18576, 15558, 18648, 15984], 'label': '31104.fx.324.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '324.ch1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.ch1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
-
id: 186245766
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.ch1', '108.cj1', '162.f1', '162.m1', '162.bf1'], 'contains': ['648.dj1', '648.dl1', '648.dm1', '972.u1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [5713, 10368, 18576, 27690, 18648, 15984], 'label': '31104.fx.324.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '324.ci1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.ci1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
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id: 186245767
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.ci1', '108.ck1', '162.f1', '162.l1', '162.bh1'], 'contains': ['648.dj1', '648.do1', '648.dp1', '972.v1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [5713, 22752, 18576, 15558, 18648, 15984], 'label': '31104.fx.324.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '324.cj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.cj1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
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id: 186245768
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.cl1', '108.cm1', '108.cn1', '162.q1'], 'contains': ['648.ea1', '648.ej1', '648.el1', '648.ev1', '648.fh1', '972.w1', '1296.bd1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [20737, 18144, 72, 36, 15552, 12940], 'label': '31104.fx.324.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.q1', 'old_label': '324.ck1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.ck1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186245769
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1'], 'contains': ['72.i1', '72.j1', '72.m1', '72.o1', '72.q1', '72.do1', '72.dq1', '72.ds1', '72.dw1', '108.f1', '108.h1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [8305, 18576, 12096, 6, 18648, 10368, 22752, 2628], 'label': '31104.fx.36.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '36.e1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
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id: 186245770
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.co1', '108.cp1', '108.cq1', '162.q1'], 'contains': ['648.el1', '648.fr1', '648.fs1', '972.x1', '1296.be1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [8209, 18144, 18216, 36, 2592, 31084], 'label': '31104.fx.324.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.q1', 'old_label': '324.cl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.cl1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186245771
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.cl1', '108.cr1', '108.cs1', '162.v1'], 'contains': ['648.b1', '648.f1', '648.n1', '648.r1', '648.bp1', '648.bw1', '648.ec1', '648.eg1', '648.em1', '648.er1', '648.fe1', '972.w1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1, 10368, 15552, 36, 16056, 2592], 'label': '31104.fx.324.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.v1', 'old_label': '324.cm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.cm1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245772
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.cn1', '108.cr1', '108.ct1', '162.w1'], 'contains': ['648.d1', '648.h1', '648.o1', '648.u1', '648.bq1', '648.by1', '648.ee1', '648.ei1', '648.en1', '648.es1', '648.ff1', '972.w1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [20737, 12384, 18144, 36, 2664, 15552], 'label': '31104.fx.324.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.w1', 'old_label': '324.cn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.cn1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245773
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.cm1', '108.cr1', '108.cu1', '162.w1'], 'contains': ['648.c1', '648.g1', '648.o1', '648.t1', '648.bq2', '648.bx1', '648.ed1', '648.eh1', '648.eo1', '648.et1', '648.fg1', '972.w1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [20737, 12384, 15552, 36, 16056, 18144], 'label': '31104.fx.324.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.w1', 'old_label': '324.co1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.co1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245774
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.cs1', '108.ct1', '108.cu1', '162.x1'], 'contains': ['648.e1', '648.i1', '648.p1', '648.w1', '648.bt1', '648.bv1', '648.ef1', '648.ek1', '648.ep1', '648.eu1', '648.fd1', '972.w1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [20737, 1728, 15552, 36, 16056, 2592], 'label': '31104.fx.324.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '324.cp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.cp1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245775
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.co1', '108.cv1', '108.cw1', '162.v1'], 'contains': ['648.q1', '648.r1', '648.bz1', '648.ca1', '648.em1', '648.fj1', '648.fk1', '972.x1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [433, 10368, 2592, 36, 16056, 15552], 'label': '31104.fx.324.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.v1', 'old_label': '324.cq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.cq1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245776
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.cq1', '108.cw1', '108.cx1', '162.w1'], 'contains': ['648.s1', '648.t1', '648.cb1', '648.cc1', '648.en1', '648.fl1', '648.fn1', '972.x1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [8209, 12384, 15552, 36, 2664, 2592], 'label': '31104.fx.324.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.w1', 'old_label': '324.cr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.cr1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245777
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.cp1', '108.cw1', '108.cy1', '162.w1'], 'contains': ['648.s1', '648.u1', '648.cb2', '648.cd1', '648.eo1', '648.fm1', '648.fo1', '972.x1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [8209, 12384, 15552, 36, 16056, 2592], 'label': '31104.fx.324.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.w1', 'old_label': '324.cs1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.cs1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245778
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.cv1', '108.cx1', '108.cy1', '162.x1'], 'contains': ['648.v1', '648.w1', '648.ce1', '648.cf1', '648.ep1', '648.fp1', '648.fq1', '972.x1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [21169, 1728, 2592, 36, 16056, 15552], 'label': '31104.fx.324.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '324.ct1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.ct1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245779
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.cz1', '108.da1', '108.dd1', '162.v1'], 'contains': ['648.bp1', '648.br1', '648.ca1', '648.cj1', '648.er1', '648.ey1', '648.fk1', '972.y1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [21169, 22752, 2592, 468, 16056, 15552], 'label': '31104.fx.324.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.v1', 'old_label': '324.cu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.cu1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245780
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '6.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': ['5184.cb1', '5184.bz1', '5184.ca1', '5184.by1', '5184.bf1', '5184.be1', '5184.bg1', '5184.bl1', '5184.bk1', '5184.bn1', '5184.bm1', '5184.y1'], 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '3.b1'], 'contains': ['12.a1', '12.b1', '12.d1', '18.m1', '18.n1', '18.s1', '24.r1'], 'core': '6.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [6, 18144, 22752, 10368, 15552, 36, 12096, 432, 16056, 5712], 'label': '31104.fx.6.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': ['2.a1'], 'normal_contains': ['12.a1', '12.b1', '12.d1'], 'normalizer': '1.a1', 'old_label': '6.a1', 'projective_image': '31104.fx', 'quotient_action_image': '6.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.a1', 'subgroup_fusion': None, 'weyl_group': '31104.fx'}
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id: 186245781
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1'], 'contains': ['72.j1', '72.k1', '72.l1', '72.n1', '72.u1', '72.dp1', '72.dr1', '72.dt1', '72.dx1', '108.g1', '108.i1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [5713, 18576, 12096, 6, 18648, 10368, 22752, 2628], 'label': '31104.fx.36.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '36.f1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.f1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
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id: 186245782
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.cz1', '108.dc1', '108.de1', '162.w1'], 'contains': ['648.bq2', '648.bs1', '648.cd1', '648.cl1', '648.es1', '648.ez1', '648.fn1', '972.y1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [8209, 12384, 15552, 18612, 2664, 2592], 'label': '31104.fx.324.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.w1', 'old_label': '324.cv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.cv1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245783
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.cz1', '108.db1', '108.df1', '162.w1'], 'contains': ['648.bq1', '648.bs1', '648.cc1', '648.ck1', '648.et1', '648.fa1', '648.fo1', '972.y1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [8209, 12384, 15552, 18612, 16056, 2592], 'label': '31104.fx.324.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.w1', 'old_label': '324.cw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.cw1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245784
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.da1', '108.db1', '108.dc1', '162.q1'], 'contains': ['648.ev1', '648.ex1', '648.fs1', '972.y1', '1296.bw1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [8209, 18144, 18216, 18612, 2592, 31084], 'label': '31104.fx.324.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.q1', 'old_label': '324.cx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.cx1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
-
id: 186245785
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.dd1', '108.de1', '108.df1', '162.x1'], 'contains': ['648.bt1', '648.bu1', '648.cf1', '648.cm1', '648.eu1', '648.fb1', '648.fq1', '972.y1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [21169, 1728, 2592, 468, 16056, 15552], 'label': '31104.fx.324.cy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '324.cy1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.cy1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245786
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.dg1', '108.dh1', '108.di1', '162.q1'], 'contains': ['648.ex1', '648.fh1', '648.fr1', '972.z1', '1296.ca1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [20737, 18144, 72, 18612, 2592, 12940], 'label': '31104.fx.324.cz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.q1', 'old_label': '324.cz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.cz1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186245787
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.dj1', '108.dk1', '108.dl1', '162.x1'], 'contains': ['648.bv1', '648.ce1', '648.cg1', '648.cm1', '648.fb1', '648.fd1', '648.fp1', '972.z1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [20737, 1728, 2592, 468, 16056, 15552], 'label': '31104.fx.324.da1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '324.da1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.da1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245788
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.dg1', '108.dj1', '108.dm1', '162.v1'], 'contains': ['648.bw1', '648.bz1', '648.ch1', '648.cj1', '648.ey1', '648.fe1', '648.fj1', '972.z1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [20737, 22752, 2592, 468, 16056, 15552], 'label': '31104.fx.324.db1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.v1', 'old_label': '324.db1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.db1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245789
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.di1', '108.dk1', '108.dm1', '162.w1'], 'contains': ['648.bx1', '648.cb2', '648.ci1', '648.ck1', '648.ez1', '648.ff1', '648.fl1', '972.z1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [20737, 12384, 15552, 18612, 2664, 2592], 'label': '31104.fx.324.dc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.w1', 'old_label': '324.dc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.dc1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245790
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.dh1', '108.dl1', '108.dm1', '162.w1'], 'contains': ['648.by1', '648.cb1', '648.ci1', '648.cl1', '648.fa1', '648.fg1', '648.fm1', '972.z1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [20737, 12384, 15552, 18612, 16056, 2592], 'label': '31104.fx.324.dd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.w1', 'old_label': '324.dd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.dd1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245791
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.z1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.dn1', '108.do1', '108.dr1', '108.ds1', '162.q1'], 'contains': ['648.el1', '648.ex1', '648.fx1', '972.ba1', '1296.ei1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [36, 18144, 72, 18576, 15552, 12940], 'label': '31104.fx.324.de1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.p1', 'old_label': '324.de1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.de1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
-
id: 186245792
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.a1', '18.b1', '18.s1'], 'contains': ['72.e1', '72.j1', '72.w1', '72.x1', '72.y1', '72.eh1', '72.ei1', '72.ek1', '72.em1', '72.et1', '72.fc1', '108.j1', '108.k1', '108.l1', '108.m1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [26047, 18576, 12096, 36, 2592, 10368, 22752, 16056], 'label': '31104.fx.36.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '36.g1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.g1', 'subgroup_fusion': None, 'weyl_group': '864.4406'}
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id: 186245793
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.dn1', '108.dp1', '108.dq1', '108.dt1', '162.o1', '162.p1', '162.r1'], 'contains': ['648.fy1', '972.ba1', '1296.ek1', '1296.jv1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [36, 15552, 2592, 12460, 2664, 18576], 'label': '31104.fx.324.df1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '324.df1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.df1', 'subgroup_fusion': None, 'weyl_group': '576.8654'}
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id: 186245794
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.do1', '108.dp1', '108.dq1', '108.du1', '108.dv1', '162.s1', '162.u1', '162.v1'], 'contains': ['648.a1', '648.cn1', '648.dd1', '648.em1', '648.ey1', '972.ba1'], 'core': '648.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [36, 22752, 15552, 16056, 18576, 18144], 'label': '31104.fx.324.dg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '324.dg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.dg1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
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id: 186245795
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.dr1', '108.ds1', '108.dt1', '108.dv1', '108.dw1', '162.w1'], 'contains': ['648.co1', '648.de1', '648.en1', '648.eo1', '648.ez1', '648.fa1', '648.fv1', '972.ba1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [36, 12384, 15552, 16056, 18576, 18144], 'label': '31104.fx.324.dh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1', 'old_label': '324.dh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.dh1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
-
id: 186245796
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.du1', '108.dw1', '162.t1', '162.x1'], 'contains': ['648.cp1', '648.cq1', '648.cr1', '648.df1', '648.dg1', '648.dh1', '648.ep1', '648.eq1', '648.fb1', '648.fc1', '648.fw1', '972.ba1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [36, 12096, 15552, 16056, 18576, 18144], 'label': '31104.fx.324.di1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '324.di1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.di1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186245797
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.gc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.dx1', '108.dy1', '108.dz1', '108.eb1', '108.ee1', '162.s1', '162.y1', '162.bf1'], 'contains': ['648.a1', '648.cs1', '648.dl1', '972.bb1'], 'core': '648.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [12138, 18576, 16056, 18144, 15552, 22752], 'label': '31104.fx.324.dj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '324.dj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.dj1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
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id: 186245798
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.gc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.dx1', '108.ea1', '162.t1', '162.z1', '162.bc1'], 'contains': ['648.ct1', '648.cu1', '648.dt1', '648.du1', '648.fw1', '972.bb1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [12138, 18576, 16056, 18144, 15552, 12096], 'label': '31104.fx.324.dk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '324.dk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.dk1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
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id: 186245799
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.q1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.dy1', '108.ec1', '108.ef1', '108.eg1', '162.o1', '162.ba1', '162.bg1'], 'contains': ['648.fy1', '972.bb1', '1296.kf1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [12138, 15552, 2592, 20812, 2664, 18576], 'label': '31104.fx.324.dl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '324.dl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.dl1', 'subgroup_fusion': None, 'weyl_group': '192.955'}
-
id: 186245800
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.dz1', '108.ed1', '162.bb1'], 'contains': ['648.gc1', '972.bb1', '1296.kg1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [17371, 15552, 2592, 29904, 15624, 15984], 'label': '31104.fx.324.dm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bi1', 'old_label': '324.dm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.dm1', 'subgroup_fusion': None, 'weyl_group': '192.955'}
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id: 186245801
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.gc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.a1', '108.ea1', '108.ec1', '108.ed1', '108.ee1', '162.u1', '162.be1', '162.bf1'], 'contains': ['648.a1', '648.cv1', '648.dm1', '972.bb1'], 'core': '648.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [17371, 22752, 2592, 16056, 15552, 18576], 'label': '31104.fx.324.dn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '324.dn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.dn1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
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id: 186245802
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.q1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.a1', '108.eb1', '108.ef1', '108.eg1', '162.p1', '162.bd1', '162.bg1'], 'contains': ['648.fy1', '972.bb1', '1296.ki1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [17371, 15552, 2592, 23836, 16056, 18576], 'label': '31104.fx.324.do1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '324.do1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.do1', 'subgroup_fusion': None, 'weyl_group': '576.8654'}
-
id: 186245803
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1', '18.c1', '18.t1'], 'contains': ['72.f1', '72.g1', '72.q1', '72.u1', '72.w1', '72.z1', '72.bb1', '72.ej1', '72.fg1', '108.n1', '108.o1', '108.p1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1, 2592, 12096, 36, 18144, 10368, 22752, 18576], 'label': '31104.fx.36.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '36.h1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.h1', 'subgroup_fusion': None, 'weyl_group': '864.4406'}
-
id: 186245804
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ep1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.eh1', '108.ei1', '108.ej1', '108.el1', '108.en1', '108.eo1', '162.u1', '162.y1', '162.bh1'], 'contains': ['648.a1', '648.cw1', '648.do1', '972.bc1'], 'core': '648.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [6, 18576, 16056, 18144, 15552, 10368], 'label': '31104.fx.324.dp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '324.dp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.dp1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
-
id: 186245805
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.q1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.eh1', '108.ek1', '108.ep1', '108.er1', '162.o1', '162.bd1', '162.bi1'], 'contains': ['648.fy1', '972.bc1', '1296.km1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [26047, 15552, 2592, 5712, 15624, 15984], 'label': '31104.fx.324.dq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '324.dq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.dq1', 'subgroup_fusion': None, 'weyl_group': '192.955'}
-
id: 186245806
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.eh1', '108.em1', '108.eq1', '108.es1', '108.et1', '162.bj1'], 'contains': ['648.ga1', '972.bc1', '1296.kn1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26047, 15552, 2592, 28464, 15624, 15984], 'label': '31104.fx.324.dr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.cd1', 'old_label': '324.dr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.dr1', 'subgroup_fusion': None, 'weyl_group': '192.955'}
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id: 186245807
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ep1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.ek1', '108.em1', '108.eo1', '108.eu1', '108.ev1', '108.ew1', '162.s1', '162.be1', '162.bh1'], 'contains': ['648.a1', '648.cx1', '648.dp1', '972.bc1'], 'core': '648.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [26047, 10368, 2592, 16056, 15552, 18576], 'label': '31104.fx.324.ds1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '324.ds1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.ds1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
-
id: 186245808
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ep1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.ei1', '108.eu1', '162.t1', '162.z1', '162.bk1'], 'contains': ['648.cy1', '648.cz1', '648.dw1', '648.dx1', '648.fw1', '972.bc1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [26047, 12096, 2592, 16056, 15552, 18576], 'label': '31104.fx.324.dt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '324.dt1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.dt1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
-
id: 186245809
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.q1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.ej1', '108.ep1', '108.es1', '108.ev1', '162.p1', '162.ba1', '162.bi1'], 'contains': ['648.fy1', '972.bc1', '1296.kr1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [26047, 15552, 2592, 23836, 16056, 18576], 'label': '31104.fx.324.du1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '324.du1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.du1', 'subgroup_fusion': None, 'weyl_group': '576.8654'}
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id: 186245810
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.dv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.el1', '108.eq1', '108.er1', '108.et1', '108.ev1', '162.bj1'], 'contains': ['648.ga1', '972.bc1', '1296.ks1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [6, 15552, 18144, 28464, 16056, 432], 'label': '31104.fx.324.dv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bh1', 'old_label': '324.dv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.dv1', 'subgroup_fusion': None, 'weyl_group': '576.8654'}
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id: 186245811
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.en1', '108.ew1', '162.bb1'], 'contains': ['648.gc1', '972.bc1', '1296.kt1', '1296.kt2'], 'core': '1944.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [6, 15552, 18144, 19536, 16056, 432], 'label': '31104.fx.324.dw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bi1', 'old_label': '324.dw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.dw1', 'subgroup_fusion': None, 'weyl_group': '192.955'}
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id: 186245812
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.dx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.ex1', '108.ey1', '108.ez1', '108.fa1', '108.fb1', '108.fc1', '108.fd1', '108.fd2', '162.v1', '162.y1', '162.be1'], 'contains': ['648.a1', '648.da1', '648.dn1', '648.er1', '648.fj1', '972.bd1'], 'core': '648.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [10405, 15552, 2592, 16056, 18576, 22752], 'label': '31104.fx.324.dx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '324.dx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.dx1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
-
id: 186245813
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.ex1', '108.fe1', '108.ff1', '108.fg1', '108.fh1', '108.fi1', '108.fi2', '108.fj1', '162.w1'], 'contains': ['648.db1', '648.dr1', '648.es1', '648.et1', '648.fl1', '648.fm1', '648.fv1', '972.bd1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [10405, 15552, 2592, 16056, 18576, 12384], 'label': '31104.fx.324.dy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bd1', 'old_label': '324.dy1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.dy1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
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id: 186245814
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.a1', '18.c1', '18.s1'], 'contains': ['72.w1', '72.bc1', '72.be1', '72.ek1', '72.fh1', '108.q1', '108.r1', '108.s1', '108.u1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [15558, 16056, 12096, 36, 2664, 22752, 10368, 18144], 'label': '31104.fx.36.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '36.i1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.i1', 'subgroup_fusion': None, 'weyl_group': '864.4406'}
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id: 186245815
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.ey1', '108.fe1', '162.x1', '162.z1'], 'contains': ['648.dc1', '648.dv1', '648.eu1', '648.fp1', '648.fw1', '972.bd1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [10405, 1728, 15552, 16056, 18576, 2592], 'label': '31104.fx.324.dz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '324.dz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.dz1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
-
id: 186245816
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.ez1', '108.ff1', '108.fg1', '108.fk1', '162.q1'], 'contains': ['648.ev1', '648.fr1', '648.fx1', '972.bd1', '1296.et1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [10405, 18144, 18216, 18576, 15552, 12940], 'label': '31104.fx.324.ea1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '324.ea1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.ea1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
-
id: 186245817
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.eb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.ba1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.fa1', '108.fb1', '108.fh1', '108.fk1', '162.r1', '162.ba1', '162.bd1'], 'contains': ['648.fy1', '972.bd1', '1296.ev1', '1296.kz1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [10405, 15552, 2592, 16080, 16056, 432], 'label': '31104.fx.324.eb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '324.eb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.eb1', 'subgroup_fusion': None, 'weyl_group': '192.955'}
-
id: 186245818
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.ec1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.fc1', '108.fi1', '108.fi2'], 'contains': ['648.ew1', '648.fu1', '648.gb1', '972.bd1', '1296.ew1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [10405, 15552, 3096, 18576, 2592, 29404], 'label': '31104.fx.324.ec1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cp1', 'old_label': '324.ec1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.ec1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186245819
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.ed1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.fd1', '108.fd2', '108.fj1', '162.bb1'], 'contains': ['648.gc1', '972.bd1', '1296.ey1', '1296.la1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [10405, 15552, 2592, 24268, 16056, 18576], 'label': '31104.fx.324.ed1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.y1', 'old_label': '324.ed1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.ed1', 'subgroup_fusion': None, 'weyl_group': '192.955'}
-
id: 186245820
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.ee1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.fl1', '108.fm1', '162.x1', '162.bc1', '162.bk1'], 'contains': ['648.di1', '648.dy1', '648.fd1', '648.fq1', '648.fw1', '972.be1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1, 15552, 2592, 16056, 18576, 1728], 'label': '31104.fx.324.ee1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '324.ee1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.ee1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
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id: 186245821
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.ef1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.fl1', '108.fn1', '108.fo1', '108.fp1', '108.fq1', '108.fr1', '162.v1', '162.bf1', '162.bh1'], 'contains': ['648.a1', '648.dj1', '648.dq1', '648.fe1', '648.fk1', '972.be1'], 'core': '648.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1, 22752, 15552, 16056, 18576, 2592], 'label': '31104.fx.324.ef1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '324.ef1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.ef1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186245822
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.eg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.fm1', '108.fr1', '108.fs1', '108.ft1', '108.fu1', '108.fv1', '162.w1'], 'contains': ['648.dk1', '648.ds1', '648.ff1', '648.fg1', '648.fn1', '648.fo1', '648.fv1', '972.be1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1, 12384, 15552, 16056, 18576, 2592], 'label': '31104.fx.324.eg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '324.eg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.eg1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245823
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.eh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.fn1', '108.fs1', '108.ft1', '108.fw1', '108.fx1', '108.fy1', '108.fz1', '162.q1'], 'contains': ['648.fh1', '648.fs1', '648.fx1', '972.be1', '1296.fi1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1, 18144, 18216, 18576, 15552, 556], 'label': '31104.fx.324.eh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.q1', 'old_label': '324.eh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.eh1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186245824
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.ei1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.fo1', '108.fp1', '108.fu1', '108.fw1', '108.fy1', '108.ga1', '108.gb1', '162.r1', '162.bg1', '162.bi1'], 'contains': ['648.fy1', '972.be1', '1296.fk1', '1296.li1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1, 15552, 2592, 5712, 16056, 432], 'label': '31104.fx.324.ei1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '324.ei1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.ei1', 'subgroup_fusion': None, 'weyl_group': '192.955'}
-
id: 186245825
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1', '18.t1'], 'contains': ['72.h1', '72.v1', '72.w1', '72.bd1', '72.bf1', '108.t1', '108.v1', '108.w1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [16057, 2592, 12096, 36, 15552, 10368, 22752, 18576], 'label': '31104.fx.36.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '36.j1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.j1', 'subgroup_fusion': None, 'weyl_group': '864.4406'}
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id: 186245826
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.fn1', '108.fs1', '108.fv1', '108.fw1', '108.fx1', '108.ga1', '108.gb1', '108.gc1', '108.gc2'], 'contains': ['648.fi1', '648.ft1', '648.fz1', '972.be1', '1296.fl1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1, 18144, 18216, 18576, 15552, 10924], 'label': '31104.fx.324.ej1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.ej1', 'old_label': '324.ej1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.ej1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186245827
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.fo1', '108.fq1', '108.fu1', '108.fw1', '108.fx1', '108.fz1', '108.ga1', '108.gc1', '108.gc2', '162.bj1'], 'contains': ['648.ga1', '972.be1', '1296.fn1', '1296.lj1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1, 15552, 2592, 76, 16056, 18576], 'label': '31104.fx.324.ek1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.bj1', 'old_label': '324.ek1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.ek1', 'subgroup_fusion': None, 'weyl_group': '192.955'}
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id: 186245828
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.el1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['81.a1', '108.gd1', '108.ge1'], 'contains': ['648.id1', '648.ie1', '648.if1', '648.jf1', '648.jk1', '648.jq1', '648.kc1', '972.bg1', '1296.lr1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [20737, 2592, 18576, 24198, 36, 16080], 'label': '31104.fx.324.el1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.el1', 'old_label': '324.el1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.el1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186245829
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.em1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.v1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.gf1', '108.gg1', '162.e1'], 'contains': ['648.gd1', '648.gf1', '648.gn1', '648.gp1', '648.gz1', '648.hc1', '648.hv1', '648.hy1', '648.ig1', '648.in1', '648.ir1', '648.iz1', '648.jc1', '648.jx1', '648.ka1', '972.bf1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 10368, 18576, 21606, 36, 16056], 'label': '31104.fx.324.em1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '324.em1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.em1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245830
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.en1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.gf1', '108.gh1', '162.c1'], 'contains': ['648.ge1', '648.gg1', '648.go1', '648.gq1', '648.ha1', '648.hb1', '648.hw1', '648.hx1', '648.ih1', '648.ip1', '648.is1', '648.ja1', '648.jb1', '648.jy1', '648.jz1', '972.bf1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 12096, 18576, 2598, 36, 16056], 'label': '31104.fx.324.en1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '324.en1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.en1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245831
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.eo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.gg1', '108.gh1', '162.e1'], 'contains': ['648.gj1', '648.gk1', '648.gn1', '648.gp1', '648.hl1', '648.hm1', '648.ht1', '648.hu1', '648.il1', '648.in2', '648.iq1', '648.jm1', '648.jo1', '648.ju1', '648.jv1', '972.bf1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 10368, 18576, 24270, 36, 2592], 'label': '31104.fx.324.eo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '324.eo1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.eo1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245832
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.ep1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.gi1', '108.gj1', '162.c1'], 'contains': ['648.ge1', '648.gg1', '648.gh1', '648.gi1', '648.gx1', '648.gy1', '648.hd1', '648.he1', '648.ih1', '648.ik1', '648.ip1', '648.iy1', '648.je1', '648.jn1', '648.ki1', '972.bg1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 12096, 18576, 6, 36, 2592], 'label': '31104.fx.324.ep1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '324.ep1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.ep1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245833
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.eq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.ge1', '108.gi1', '108.gk1', '162.e1'], 'contains': ['648.gd1', '648.gf1', '648.gl1', '648.gm1', '648.gv1', '648.gw1', '648.hp1', '648.hq1', '648.ij1', '648.il1', '648.in2', '648.jd1', '648.jl1', '648.jp1', '648.kh1', '972.bg1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 22752, 18576, 24198, 36, 16056], 'label': '31104.fx.324.eq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '324.eq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.eq1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245834
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.er1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.n1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.gd1', '108.gj1', '108.gk1', '162.e1'], 'contains': ['648.gj1', '648.gk1', '648.gl1', '648.gm1', '648.hj1', '648.hk1', '648.hn1', '648.ho1', '648.ig1', '648.im1', '648.in1', '648.iu1', '648.jr1', '648.jt1', '648.kb1', '972.bg1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 22752, 18576, 24198, 36, 2592], 'label': '31104.fx.324.er1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '324.er1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.er1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 186245835
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.es1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.gl1', '108.gm1', '162.e1'], 'contains': ['648.gr1', '648.gs1', '648.gv1', '648.gw1', '648.ht1', '648.hu1', '648.hz1', '648.ia1', '648.iu1', '648.iv1', '648.jc1', '648.jw1', '648.jx1', '648.kb1', '648.kj1', '972.bh1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 10368, 18576, 24198, 2628, 16056], 'label': '31104.fx.324.es1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '324.es1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.es1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
-
id: 186245836
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.b1', '18.d1', '18.w1'], 'contains': ['72.i1', '72.k1', '72.x1', '72.y1', '72.z1', '72.en1', '72.eo1', '72.eq1', '72.ez1', '108.x1', '108.bb1', '108.bc1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [26485, 22752, 18576, 12138, 2592, 10368, 12096, 16056], 'label': '31104.fx.36.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '36.k1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.k1', 'subgroup_fusion': None, 'weyl_group': '576.7160'}
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id: 186245837
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.et1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.gl1', '108.gn1', '162.c1'], 'contains': ['648.gt1', '648.gu1', '648.gx1', '648.gy1', '648.hw1', '648.hx1', '648.ib1', '648.ic1', '648.iw1', '648.iy1', '648.jb1', '648.jy1', '648.kf1', '648.ki1', '648.kl1', '972.bh1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 12096, 18576, 6, 108, 2592], 'label': '31104.fx.324.et1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '324.et1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.et1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
-
id: 186245838
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.eu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.go1', '108.gp1', '162.c1'], 'contains': ['648.gt1', '648.gu1', '648.ha1', '648.hb1', '648.hd1', '648.he1', '648.hf1', '648.hg1', '648.iw1', '648.ja1', '648.je1', '648.ji2', '648.jn1', '648.jz1', '648.kl1', '972.bi1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 12096, 18576, 78, 108, 2592], 'label': '31104.fx.324.eu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '324.eu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.eu1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
-
id: 186245839
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.ev1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.gm1', '108.gn1', '162.e1'], 'contains': ['648.hh1', '648.hi1', '648.hj1', '648.hk1', '648.hv1', '648.hy1', '648.hz1', '648.ia1', '648.jj1', '648.jl1', '648.jo1', '648.ju1', '648.ke1', '648.kh1', '648.kj2', '972.bh1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 22752, 18576, 24198, 2628, 16056], 'label': '31104.fx.324.ev1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '324.ev1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.ev1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
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id: 186245840
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.ew1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.go1', '108.gq1', '162.e1'], 'contains': ['648.gr1', '648.gs1', '648.gz1', '648.hc1', '648.hn1', '648.ho1', '648.hr1', '648.hs1', '648.jd1', '648.jh1', '648.jj1', '648.jm1', '648.jp1', '648.jv1', '648.kj2', '972.bi1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 10368, 18576, 24270, 108, 2592], 'label': '31104.fx.324.ew1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '324.ew1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.ew1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
-
id: 186245841
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '324.ex1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.gp1', '108.gq1', '162.e1'], 'contains': ['648.hh1', '648.hi1', '648.hl1', '648.hm1', '648.hp1', '648.hq1', '648.hr1', '648.hs1', '648.iv1', '648.iz1', '648.jr1', '648.js1', '648.jt1', '648.ka1', '648.kj1', '972.bi1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 22752, 18576, 24270, 108, 2592], 'label': '31104.fx.324.ex1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '324.ex1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.ex1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
-
id: 186245842
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '384.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.df1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.h1', '128.a1', '192.a1', '192.c1', '192.m1', '192.r1', '192.s1'], 'contains': ['1152.a1', '1152.h1', '1152.j1', '1152.l1', '1152.m1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [10924, 12096, 10368], 'label': '31104.fx.384.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1', 'old_label': '384.a1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.a1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
-
id: 186245843
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '384.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.i1', '96.n1', '128.a1', '192.d1', '192.e1', '192.f1', '192.i1', '192.l1', '192.n1', '192.t1'], 'contains': ['1152.a1', '1152.b1', '1152.c1', '1152.i1', '1152.k1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [5712, 12096, 22752], 'label': '31104.fx.384.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.d1', 'old_label': '384.b1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.b1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
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id: 186245844
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '384.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.j1', '96.k1', '128.a1', '192.o1'], 'contains': ['1152.h1', '1152.j1', '1152.k1', '1152.o1', '1152.q1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [6484, 29904, 10368], 'label': '31104.fx.384.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.d1', 'old_label': '384.c1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.c1', 'subgroup_fusion': None, 'weyl_group': '54.14'}
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id: 186245845
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '384.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.l1', '128.a1', '192.b1', '192.g1', '192.j1', '192.p1', '192.u1'], 'contains': ['1152.d1', '1152.e1', '1152.h1', '1152.i1', '1152.n1', '1152.p1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [18580, 5712, 22752, 10368], 'label': '31104.fx.384.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.d1', 'old_label': '384.d1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.d1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186245846
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '384.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.m1', '128.a1', '192.h1', '192.k1', '192.q1'], 'contains': ['1152.f1', '1152.g1', '1152.i1', '1152.j1', '1152.k1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [18580, 29904, 10368], 'label': '31104.fx.384.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.d1', 'old_label': '384.e1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.e1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
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id: 186245847
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.d1', '18.e1', '18.s1'], 'contains': ['72.x1', '72.ba1', '72.be1', '72.et1', '72.fh1', '108.y1', '108.bd1', '108.be1', '108.bf1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [10495, 18576, 12096, 15588, 2592, 10368, 22752, 16056], 'label': '31104.fx.36.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '36.l1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.l1', 'subgroup_fusion': None, 'weyl_group': '864.4406'}
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id: 186245848
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.a1', '216.co1', '216.cp1', '216.ez1'], 'contains': ['864.a1', '864.k1', '864.bm1', '864.ef1', '864.eg1', '864.ev1', '864.ew1', '1296.a1', '1296.d1', '1296.e1', '1296.g1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [36, 10368, 16056, 2592, 12096], 'label': '31104.fx.432.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.du1', 'old_label': '432.a1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 186245849
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.a1', '216.d1', '216.co1', '216.ez1'], 'contains': ['864.b1', '864.k1', '864.bm2', '864.eg1', '864.ew2', '1296.a1', '1296.f1', '1296.g1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [36, 10368, 16056, 15552, 12096], 'label': '31104.fx.432.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.be1', 'old_label': '432.b1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186245850
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.a1', '216.c1', '216.cq1', '216.fa1'], 'contains': ['864.c1', '864.l1', '864.bn1', '864.eh1', '864.ex1', '1296.a1', '1296.b1', '1296.c1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [36, 10368, 16056, 15552, 22752], 'label': '31104.fx.432.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bd1', 'old_label': '432.c1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.c1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
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id: 186245851
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.a1', '216.cs1', '216.fd1'], 'contains': ['864.d1', '864.n1', '864.bp1', '864.ei1', '864.ej1', '864.ey1', '864.ez1', '1296.b1', '1296.d1', '1296.g1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [36, 12384, 15552, 504, 12096], 'label': '31104.fx.432.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.dw1', 'old_label': '432.d1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.d1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 186245852
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.a1', '216.e1', '216.cr1', '216.fd1'], 'contains': ['864.e1', '864.m1', '864.bo1', '864.ej1', '864.ez2', '1296.b1', '1296.e1', '1296.f1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [36, 12384, 2592, 18648, 12096], 'label': '31104.fx.432.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '432.e1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.e1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186245853
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.a1', '216.f1', '216.cs1', '216.fb1'], 'contains': ['864.f1', '864.o1', '864.bq1', '864.ei1', '864.ey2', '1296.c1', '1296.d1', '1296.f1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [36, 12384, 18576, 18144, 12096], 'label': '31104.fx.432.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '432.f1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.f1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186245854
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.a1', '216.cr1', '216.cs1', '216.fc1'], 'contains': ['864.g1', '864.o1', '864.bq2', '864.ej1', '864.ez3', '1296.c1', '1296.e1', '1296.g1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [36, 12384, 16056, 18216, 12096], 'label': '31104.fx.432.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.dw1', 'old_label': '432.g1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.g1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 186245855
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.b1', '216.c1', '216.g1', '216.fe1'], 'contains': ['864.c1', '864.p1', '864.ce1', '1296.h1', '1296.i1', '1296.j1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [10405, 15552, 16056, 22752, 10368], 'label': '31104.fx.432.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cr1', 'old_label': '432.h1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.h1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186245856
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.b1', '216.d1', '216.h1', '216.ff1'], 'contains': ['864.b1', '864.q1', '864.bz1', '1296.h1', '1296.k1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [10405, 1728, 16056, 10368, 15552], 'label': '31104.fx.432.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bc1', 'old_label': '432.i1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.i1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186245857
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.b1', '216.e1', '216.i1', '216.fj1'], 'contains': ['864.e1', '864.t1', '864.cg1', '1296.i1', '1296.k1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [10405, 1728, 16056, 12384, 15552], 'label': '31104.fx.432.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bc1', 'old_label': '432.j1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.j1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186245858
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.a1', '18.e1', '18.w1'], 'contains': ['72.x1', '72.bd1', '72.be1', '108.z1', '108.bg1', '108.bi1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [10933, 15984, 18576, 12138, 18648, 10368, 12096, 22752], 'label': '31104.fx.36.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '36.m1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.m1', 'subgroup_fusion': None, 'weyl_group': '576.7160'}
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id: 186245859
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.b1', '216.f1', '216.j1', '216.fi1'], 'contains': ['864.f1', '864.u1', '864.ch1', '1296.j1', '1296.k1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [10405, 1728, 2664, 12384, 18144], 'label': '31104.fx.432.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bc1', 'old_label': '432.k1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.k1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186245860
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.c1', '216.co1', '216.df1', '216.fr1'], 'contains': ['864.a1', '864.bc1', '864.bm2', '864.ev1', '864.ew2', '864.ff1', '864.fg1', '1296.l1', '1296.o1', '1296.p1', '1296.r1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [468, 10368, 16056, 2592, 12096], 'label': '31104.fx.432.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.du1', 'old_label': '432.l1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.l1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 186245861
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.l2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.c1', '216.cp1', '216.de1', '216.fr1'], 'contains': ['864.a1', '864.bc2', '864.bm1', '864.ev1', '864.ew1', '864.ff2', '864.fg2', '1296.l1', '1296.o1', '1296.p2', '1296.r2'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [16020, 10368, 16056, 2592, 12096], 'label': '31104.fx.432.l2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.du1', 'old_label': '432.l2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.l2', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 186245862
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.c1', '216.co1', '216.de1', '216.fr1'], 'contains': ['864.b1', '864.bc1', '864.bm1', '864.ew1', '864.ew2', '864.fg1', '864.fg2', '1296.l1', '1296.q1', '1296.r1', '1296.r2'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [18612, 22752, 504, 3096, 12096], 'label': '31104.fx.432.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.du1', 'old_label': '432.m1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.m1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
-
id: 186245863
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.c1', '216.cq1', '216.dg1', '216.fs1'], 'contains': ['864.c1', '864.bd1', '864.bn1', '864.ex1', '864.fh1', '1296.l1', '1296.m1', '1296.n1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [18612, 10368, 16056, 15552, 22752], 'label': '31104.fx.432.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.dv1', 'old_label': '432.n1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.n1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 186245864
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.c1', '216.cs1', '216.di1', '216.fv1'], 'contains': ['864.d1', '864.bf1', '864.bp1', '864.ey2', '864.ez3', '864.fi1', '864.fj1', '1296.m1', '1296.o1', '1296.r1', '1296.r2'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [108, 12384, 15552, 504, 12096], 'label': '31104.fx.432.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.dw1', 'old_label': '432.o1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.o1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 186245865
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.c1', '216.cr1', '216.dh1', '216.fv1'], 'contains': ['864.e1', '864.be1', '864.bo1', '864.ez3', '864.fj1', '1296.m1', '1296.p1', '1296.p2', '1296.q1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [108, 12384, 2592, 18648, 12096], 'label': '31104.fx.432.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.dw1', 'old_label': '432.p1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.p1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 186245866
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.c1', '216.cs1', '216.di1', '216.ft1'], 'contains': ['864.f1', '864.bg1', '864.bq2', '864.ey1', '864.fi1', '1296.n1', '1296.o1', '1296.q1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [3132, 12384, 18576, 18144, 12096], 'label': '31104.fx.432.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.dw1', 'old_label': '432.q1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.q1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 186245867
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.c1', '216.cr1', '216.di1', '216.fu1'], 'contains': ['864.g1', '864.bg2', '864.bq2', '864.ez2', '864.fj1', '1296.n1', '1296.p2', '1296.r1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [468, 12384, 16056, 18216, 12096], 'label': '31104.fx.432.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.dw1', 'old_label': '432.r1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.r1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 186245868
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.r2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.c1', '216.cs1', '216.dh1', '216.fu1'], 'contains': ['864.g1', '864.bg1', '864.bq1', '864.ez1', '864.fj1', '1296.n1', '1296.p1', '1296.r2'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [18612, 12384, 16056, 18216, 12096], 'label': '31104.fx.432.r2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.dw1', 'old_label': '432.r2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.r2', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 186245869
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.a1', '18.d1', '18.z1'], 'contains': ['72.x1', '72.bc1', '72.bf1', '108.ba1', '108.bh1', '108.bj1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [21265, 15984, 18576, 12138, 18648, 10368, 22752, 12096], 'label': '31104.fx.36.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '36.n1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.n1', 'subgroup_fusion': None, 'weyl_group': '576.7160'}
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id: 186245870
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.d1', '216.de1', '216.df1', '216.ez1'], 'contains': ['864.a1', '864.bc1', '864.bh1', '864.ev1', '864.ew2', '864.fa1', '864.fb1', '1296.s1', '1296.v1', '1296.w1', '1296.y1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [15588, 10368, 16056, 2592, 12096], 'label': '31104.fx.432.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.du1', 'old_label': '432.s1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.s1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 186245871
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.d1', '216.h1', '216.de1', '216.ez1'], 'contains': ['864.b1', '864.bc2', '864.bh1', '864.ew1', '864.fb1', '1296.s1', '1296.x1', '1296.y1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [2628, 10368, 16056, 15552, 12096], 'label': '31104.fx.432.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.be1', 'old_label': '432.t1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.t1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186245872
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.d1', '216.g1', '216.dg1', '216.fa1'], 'contains': ['864.c1', '864.bd1', '864.bi1', '864.ex1', '864.fc1', '1296.s1', '1296.t1', '1296.u1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [2628, 10368, 16056, 15552, 22752], 'label': '31104.fx.432.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bd1', 'old_label': '432.u1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.u1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
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id: 186245873
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.d1', '216.di1', '216.fd1'], 'contains': ['864.d1', '864.bf1', '864.bk1', '864.ey1', '864.ez2', '864.fd1', '864.fe1', '1296.t1', '1296.v1', '1296.y1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [18180, 12384, 15552, 504, 12096], 'label': '31104.fx.432.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.dw1', 'old_label': '432.v1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.v1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 186245874
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.d1', '216.i1', '216.dh1', '216.fd1'], 'contains': ['864.e1', '864.be1', '864.bj1', '864.ez1', '864.fe1', '1296.t1', '1296.w1', '1296.x1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [18180, 12384, 2592, 18648, 12096], 'label': '31104.fx.432.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '432.w1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.w1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186245875
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.d1', '216.j1', '216.di1', '216.fb1'], 'contains': ['864.f1', '864.bg2', '864.bl1', '864.ey2', '864.fd1', '1296.u1', '1296.v1', '1296.x1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [18684, 12384, 18576, 18144, 12096], 'label': '31104.fx.432.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '432.x1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.x1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186245876
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.d1', '216.dh1', '216.di1', '216.fc1'], 'contains': ['864.g1', '864.bg1', '864.bl1', '864.ez3', '864.fe1', '1296.u1', '1296.w1', '1296.y1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [18180, 12384, 16056, 18216, 12096], 'label': '31104.fx.432.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.dw1', 'old_label': '432.y1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.y1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 186245877
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.e1', '216.d1', '216.h1', '216.fw1'], 'contains': ['864.b1', '864.br1', '864.ca1', '1296.z1', '1296.ba1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1, 22752, 16056, 1728, 15552], 'label': '31104.fx.432.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cs1', 'old_label': '432.z1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.z1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186245878
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.e1', '216.e1', '216.i1', '216.fy1'], 'contains': ['864.e1', '864.bs1', '864.ci1', '1296.z1', '1296.bb1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1, 12384, 16056, 1728, 15552], 'label': '31104.fx.432.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cu1', 'old_label': '432.ba1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ba1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186245879
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.e1', '216.f1', '216.j1', '216.fx1'], 'contains': ['864.f1', '864.bt1', '864.cj1', '1296.z1', '1296.bc1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1, 12384, 2664, 1728, 18144], 'label': '31104.fx.432.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ct1', 'old_label': '432.bb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bb1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186245880
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1', '18.e1', '18.z1'], 'contains': ['72.l1', '72.m1', '72.x1', '72.bb1', '72.ep1', '72.ew1', '108.bk1', '108.bl1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [5713, 12096, 18576, 12138, 2592, 10368, 22752, 16056], 'label': '31104.fx.36.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '36.o1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.o1', 'subgroup_fusion': None, 'weyl_group': '576.7160'}
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id: 186245881
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.e1', '216.c1', '216.g1', '216.ga1'], 'contains': ['864.c1', '864.bv1', '864.cf1', '1296.ba1', '1296.bb1', '1296.bc1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1, 10368, 16056, 15552, 22752], 'label': '31104.fx.432.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bc1', 'old_label': '432.bc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bc1', 'subgroup_fusion': None, 'weyl_group': '72.49'}
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id: 186246743
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.gd1', '288.r1', '288.s1', '432.gz1'], 'contains': ['1728.j1', '1728.dk1', '2592.bl1', '2592.bo1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [1, 15552, 10924, 12384], 'label': '31104.fx.864.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.cp1', 'old_label': '864.by1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.by1', 'subgroup_fusion': None, 'weyl_group': '108.25'}
-
id: 186245882
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.cl1', '144.f1', '216.eb1'], 'contains': ['864.h1', '864.r1', '864.bu1', '864.gs1', '864.ii1', '1296.bd1', '1296.bf1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [1, 10368, 36, 15552, 12940], 'label': '31104.fx.432.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.eb1', 'old_label': '432.bd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bd1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245883
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.cm1', '144.f1', '216.ef1'], 'contains': ['864.i1', '864.v1', '864.bw1', '864.gv1', '864.ij1', '1296.bd1', '1296.bh1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [20737, 2016, 36, 15552, 10924], 'label': '31104.fx.432.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ef1', 'old_label': '432.be1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.be1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245884
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.cn1', '144.f1', '144.g1', '216.eg1'], 'contains': ['864.j1', '864.w1', '864.bx1', '864.gw1', '864.ik1', '1296.bd1', '1296.bg1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [20737, 12384, 36, 15552, 556], 'label': '31104.fx.432.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.eg1', 'old_label': '432.bf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bf1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245885
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.co1', '144.h1', '216.eb1'], 'contains': ['864.h1', '864.cb1', '864.cc1', '1296.be1', '1296.bj1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [505, 10368, 36, 15552, 31084], 'label': '31104.fx.432.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.eb1', 'old_label': '432.bg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bg1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245886
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.cp1', '144.h1', '216.ef1'], 'contains': ['864.i1', '864.ck1', '864.cl1', '1296.be1', '1296.bl1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [21241, 2016, 36, 15552, 29068], 'label': '31104.fx.432.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ef1', 'old_label': '432.bh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bh1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245887
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.cq1', '144.h1', '144.i1', '216.eg1'], 'contains': ['864.j1', '864.cm1', '864.cn1', '1296.be1', '1296.bk1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [21241, 12384, 36, 15552, 18700], 'label': '31104.fx.432.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.eg1', 'old_label': '432.bi1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bi1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245888
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.f1', '144.j1', '216.c1', '216.o1', '216.el1'], 'contains': ['864.l1', '864.p1', '864.bv1', '864.hb1', '864.ig1', '1296.bf1', '1296.bg1', '1296.bh1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1, 10368, 36, 18144, 22752], 'label': '31104.fx.432.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cr1', 'old_label': '432.bj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bj1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
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id: 186245889
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.j1', '216.d1', '216.p1', '216.em1'], 'contains': ['864.k1', '864.q1', '864.br1', '864.hc1', '864.il1', '1296.bf1', '1296.bi1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [20737, 22752, 36, 18144, 1728], 'label': '31104.fx.432.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cs1', 'old_label': '432.bk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bk1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245890
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.g1', '144.j1', '216.e1', '216.q1', '216.en1'], 'contains': ['864.m1', '864.t1', '864.bs1', '864.hd1', '864.im1', '1296.bg1', '1296.bi1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [20737, 12384, 36, 15552, 1728], 'label': '31104.fx.432.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cu1', 'old_label': '432.bl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bl1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245891
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': ['5184.s1', '5184.bu1', '5184.bu3', '5184.br2', '5184.bu2', '5184.br1', '5184.bj1', '5184.bn1', '5184.bm1', '5184.bd1', '5184.bg1'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1', '3.a1'], 'contains': ['12.c1', '12.e1', '18.bf1', '18.bg1', '96.z1'], 'core': '6.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 18144, 22752, 10368, 15552, 12138, 5712, 18576, 16056, 76], 'label': '31104.fx.6.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': ['2.d1'], 'normal_contains': ['12.c1', '12.e1'], 'normalizer': '1.a1', 'old_label': '6.b1', 'projective_image': '31104.fx', 'quotient_action_image': '6.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.b1', 'subgroup_fusion': None, 'weyl_group': '31104.fx'}
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id: 186245892
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.d1', '18.f1', '18.s1'], 'contains': ['72.y1', '72.ba1', '72.bc1', '72.fc1', '72.fh1', '108.bm1', '108.bn1', '108.bo1', '108.bu1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [6, 16056, 12096, 15588, 2664, 22752, 10368, 18144], 'label': '31104.fx.36.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '36.p1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.p1', 'subgroup_fusion': None, 'weyl_group': '864.4406'}
-
id: 186245893
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.j1', '216.f1', '216.q1', '216.eo1'], 'contains': ['864.o1', '864.u1', '864.bt1', '864.hd1', '864.im2', '1296.bh1', '1296.bi1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [20737, 12384, 36, 18144, 1728], 'label': '31104.fx.432.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ct1', 'old_label': '432.bm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bm1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245894
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.k1', '216.d1', '216.s1', '216.em1'], 'contains': ['864.k1', '864.bz1', '864.ca1', '1296.bj1', '1296.bm1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [15625, 10368, 36, 18144, 1728], 'label': '31104.fx.432.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cs1', 'old_label': '432.bn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bn1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245895
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.h1', '144.k1', '216.c1', '216.u1', '216.el1'], 'contains': ['864.l1', '864.ce1', '864.cf1', '1296.bj1', '1296.bk1', '1296.bl1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [15625, 10368, 36, 18144, 22752], 'label': '31104.fx.432.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cr1', 'old_label': '432.bo1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bo1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
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id: 186245896
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.i1', '144.k1', '216.e1', '216.w1', '216.en1'], 'contains': ['864.m1', '864.cg1', '864.ci1', '1296.bk1', '1296.bm1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5689, 12384, 36, 15552, 1728], 'label': '31104.fx.432.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cu1', 'old_label': '432.bp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bp1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245897
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.k1', '216.f1', '216.x1', '216.eo1'], 'contains': ['864.o1', '864.ch1', '864.cj1', '1296.bl1', '1296.bm1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [23401, 12384, 36, 18144, 1728], 'label': '31104.fx.432.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ct1', 'old_label': '432.bq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bq1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245898
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.m1', '216.g1', '216.o1', '216.ep1'], 'contains': ['864.p1', '864.bd1', '864.bv1', '864.ig1', '864.ih1', '1296.bn1', '1296.bo1', '1296.bp1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1, 10368, 2628, 18144, 22752], 'label': '31104.fx.432.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cr1', 'old_label': '432.br1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.br1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
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id: 186245899
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.l1', '144.n1', '216.g1', '216.bq1', '216.el1'], 'contains': ['864.p1', '864.bi1', '864.cf1', '1296.bq1', '1296.br1', '1296.bs1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [15625, 10368, 18252, 18144, 22752], 'label': '31104.fx.432.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cr1', 'old_label': '432.bs1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bs1', 'subgroup_fusion': None, 'weyl_group': '72.49'}
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id: 186245900
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.o1', '216.c1', '216.bq1', '216.ep1'], 'contains': ['864.p1', '864.bn1', '864.cf1', '1296.bt1', '1296.bu1', '1296.bv1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [15625, 10368, 15660, 18144, 22752], 'label': '31104.fx.432.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cr1', 'old_label': '432.bt1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bt1', 'subgroup_fusion': None, 'weyl_group': '72.49'}
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id: 186245901
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.da1', '144.l1', '216.eb1'], 'contains': ['864.r1', '864.z1', '864.cc1', '1296.bq1', '1296.bw1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [505, 10368, 18684, 15552, 31084], 'label': '31104.fx.432.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.eb1', 'old_label': '432.bu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bu1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 186245902
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.db1', '144.l1', '216.ef1'], 'contains': ['864.v1', '864.ba1', '864.cl1', '1296.bs1', '1296.bw1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [21241, 2016, 18684, 15552, 29068], 'label': '31104.fx.432.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ef1', 'old_label': '432.bv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bv1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245903
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.a1', '18.f1', '18.w1'], 'contains': ['72.y1', '72.bc1', '72.bd1', '108.bp1', '108.br1', '108.bv1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [10933, 15984, 18576, 27690, 18648, 10368, 12096, 22752], 'label': '31104.fx.36.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '36.q1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.q1', 'subgroup_fusion': None, 'weyl_group': '576.7160'}
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id: 186245904
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.dc1', '144.l1', '144.p1', '216.eg1'], 'contains': ['864.w1', '864.bb1', '864.cn1', '1296.br1', '1296.bw1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [21241, 12384, 18684, 15552, 18700], 'label': '31104.fx.432.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.eg1', 'old_label': '432.bw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bw1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245905
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.m1', '216.h1', '216.p1', '216.et1'], 'contains': ['864.q1', '864.bc2', '864.br1', '864.il1', '864.in1', '1296.bn1', '1296.bx1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1, 10368, 2628, 18144, 1728], 'label': '31104.fx.432.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cs1', 'old_label': '432.bx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bx1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245906
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.m1', '216.i1', '216.q1', '216.eu1'], 'contains': ['864.t1', '864.be1', '864.bs1', '864.im2', '864.io1', '1296.bo1', '1296.bx1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [20737, 12384, 2628, 15552, 1728], 'label': '31104.fx.432.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cu1', 'old_label': '432.by1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.by1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245907
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.m1', '216.j1', '216.q1', '216.ev1'], 'contains': ['864.u1', '864.bg2', '864.bt1', '864.im1', '864.io1', '1296.bp1', '1296.bx1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [20737, 12384, 15588, 18144, 1728], 'label': '31104.fx.432.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ct1', 'old_label': '432.bz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bz1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245908
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.n1', '216.h1', '216.bs1', '216.em1'], 'contains': ['864.q1', '864.bh1', '864.ca1', '1296.bq1', '1296.by1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [15625, 10368, 18252, 18144, 1728], 'label': '31104.fx.432.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cs1', 'old_label': '432.ca1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ca1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245909
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.n1', '144.p1', '216.i1', '216.bt2', '216.en1'], 'contains': ['864.t1', '864.bj1', '864.ci1', '1296.br1', '1296.by1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5689, 12384, 18684, 15552, 1728], 'label': '31104.fx.432.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cu1', 'old_label': '432.cb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cb1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245910
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.n1', '216.j1', '216.bt1', '216.eo1'], 'contains': ['864.u1', '864.bl1', '864.cj1', '1296.bs1', '1296.by1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [23401, 12384, 18252, 18144, 1728], 'label': '31104.fx.432.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ct1', 'old_label': '432.cc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cc1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245911
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.o1', '216.d1', '216.bs1', '216.et1'], 'contains': ['864.q1', '864.bm2', '864.ca1', '1296.bt1', '1296.bz1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [15625, 10368, 15660, 18144, 1728], 'label': '31104.fx.432.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cs1', 'old_label': '432.cd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cd1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245912
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.o1', '216.e1', '216.bt2', '216.eu1'], 'contains': ['864.t1', '864.bo1', '864.ci1', '1296.bu1', '1296.bz1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5689, 12384, 16092, 15552, 1728], 'label': '31104.fx.432.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cu1', 'old_label': '432.ce1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ce1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245913
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.o1', '216.f1', '216.bt1', '216.ev1'], 'contains': ['864.u1', '864.bq1', '864.cj1', '1296.bv1', '1296.bz1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [23401, 12384, 2700, 18144, 1728], 'label': '31104.fx.432.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ct1', 'old_label': '432.cf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cf1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245914
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.a1', '18.d1', '18.bm1'], 'contains': ['72.y1', '72.be1', '72.bf1', '108.bq1', '108.bs1', '108.bw1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [21265, 18576, 12096, 15558, 15984, 10368, 22752, 18648], 'label': '31104.fx.36.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '36.r1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.r1', 'subgroup_fusion': None, 'weyl_group': '1728.39001'}
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id: 186245915
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.dg1', '144.r1', '216.eb1'], 'contains': ['864.z1', '864.bu1', '864.cb1', '1296.ca1', '1296.cg1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [1, 10368, 18684, 15552, 12940], 'label': '31104.fx.432.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.eb1', 'old_label': '432.cg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cg1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245916
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.dh1', '144.r1', '216.ef1'], 'contains': ['864.ba1', '864.bw1', '864.ck1', '1296.ca1', '1296.ci1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [20737, 2016, 18684, 15552, 10924], 'label': '31104.fx.432.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ef1', 'old_label': '432.ch1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ch1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245917
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.di1', '144.q1', '144.r1', '216.eg1'], 'contains': ['864.bb1', '864.bx1', '864.cm1', '1296.ca1', '1296.ch1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [20737, 12384, 18684, 15552, 556], 'label': '31104.fx.432.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.eg1', 'old_label': '432.ci1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ci1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245918
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.s1', '216.h1', '216.s1', '216.et1'], 'contains': ['864.bc2', '864.bz1', '864.ca1', '1296.cb1', '1296.ce1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [15625, 10368, 2628, 18144, 1728], 'label': '31104.fx.432.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cs1', 'old_label': '432.cj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cj1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245919
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.s1', '216.g1', '216.u1', '216.ep1'], 'contains': ['864.bd1', '864.ce1', '864.cf1', '1296.cb1', '1296.cc1', '1296.cd1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [15625, 10368, 2628, 18144, 22752], 'label': '31104.fx.432.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cr1', 'old_label': '432.ck1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ck1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
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id: 186245920
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.s1', '216.i1', '216.w1', '216.eu1'], 'contains': ['864.be1', '864.cg1', '864.ci1', '1296.cc1', '1296.ce1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5689, 12384, 2628, 15552, 1728], 'label': '31104.fx.432.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cu1', 'old_label': '432.cl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cl1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245921
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.s1', '216.j1', '216.x1', '216.ev1'], 'contains': ['864.bg2', '864.ch1', '864.cj1', '1296.cd1', '1296.ce1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [23401, 12384, 15588, 18144, 1728], 'label': '31104.fx.432.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ct1', 'old_label': '432.cm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cm1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245922
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.t1', '216.h1', '216.bw1', '216.em1'], 'contains': ['864.bh1', '864.br1', '864.bz1', '1296.cf1', '1296.cg1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1, 10368, 18252, 18144, 1728], 'label': '31104.fx.432.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cs1', 'old_label': '432.cn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cn1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 186245923
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.q1', '144.t1', '216.i1', '216.bx1', '216.en1'], 'contains': ['864.bj1', '864.bs1', '864.cg1', '1296.cf1', '1296.ch1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [20737, 12384, 18684, 15552, 1728], 'label': '31104.fx.432.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cu1', 'old_label': '432.co1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.co1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245924
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.t1', '216.j1', '216.by1', '216.eo1'], 'contains': ['864.bl1', '864.bt1', '864.ch1', '1296.cf1', '1296.ci1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [20737, 12384, 18252, 18144, 1728], 'label': '31104.fx.432.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ct1', 'old_label': '432.cp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cp1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245925
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1', '18.f1', '18.bm1'], 'contains': ['72.n1', '72.o1', '72.y1', '72.bb1', '72.fa1', '72.ff1', '108.bt1', '108.bx1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [5713, 18576, 12096, 6, 2592, 10368, 22752, 16056], 'label': '31104.fx.36.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '36.s1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.s1', 'subgroup_fusion': None, 'weyl_group': '1728.39001'}
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id: 186245926
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.r1', '144.t1', '216.g1', '216.bz1', '216.el1'], 'contains': ['864.bi1', '864.bv1', '864.ce1', '1296.cg1', '1296.ch1', '1296.ci1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1, 10368, 18252, 18144, 22752], 'label': '31104.fx.432.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cr1', 'old_label': '432.cq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cq1', 'subgroup_fusion': None, 'weyl_group': '72.49'}
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id: 186245927
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.u1', '216.d1', '216.bw1', '216.et1'], 'contains': ['864.bm2', '864.br1', '864.bz1', '1296.cj1', '1296.ck1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1, 10368, 15660, 18144, 1728], 'label': '31104.fx.432.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cs1', 'old_label': '432.cr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cr1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245928
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.u1', '216.e1', '216.bx1', '216.eu1'], 'contains': ['864.bo1', '864.bs1', '864.cg1', '1296.cj1', '1296.cl1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [20737, 12384, 16092, 15552, 1728], 'label': '31104.fx.432.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cu1', 'old_label': '432.cs1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cs1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245929
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.u1', '216.f1', '216.by1', '216.ev1'], 'contains': ['864.bq1', '864.bt1', '864.ch1', '1296.cj1', '1296.cm1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [20737, 12384, 2700, 18144, 1728], 'label': '31104.fx.432.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ct1', 'old_label': '432.ct1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ct1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245930
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.u1', '216.c1', '216.bz1', '216.ep1'], 'contains': ['864.bn1', '864.bv1', '864.ce1', '1296.ck1', '1296.cl1', '1296.cm1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1, 10368, 15660, 18144, 22752], 'label': '31104.fx.432.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cr1', 'old_label': '432.cu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cu1', 'subgroup_fusion': None, 'weyl_group': '72.49'}
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id: 186245931
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.v1', '216.k1', '216.l1', '216.p1', '216.r1', '216.s1', '216.cp1', '216.ez1'], 'contains': ['864.k1', '864.bc2', '864.cr1', '864.ef1', '864.fa1', '1296.cn1', '1296.cp1', '1296.cr1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [36, 10368, 18648, 18576, 12096], 'label': '31104.fx.432.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '432.cv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cv1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245932
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.v1', '216.m1', '216.co1', '216.ez1'], 'contains': ['864.k1', '864.bc1', '864.cs1', '864.eg1', '864.fb1', '1296.cn1', '1296.cq1', '1296.cr1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [36, 10368, 18144, 16056, 12096], 'label': '31104.fx.432.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bb1', 'old_label': '432.cw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cw1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186245933
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.bd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.v1', '216.n1', '216.o1', '216.t1', '216.u1', '216.cq1', '216.fa1'], 'contains': ['864.l1', '864.bd1', '864.ct1', '864.eh1', '864.fc1', '1296.cn1', '1296.co1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [36, 10368, 18144, 16056, 22752], 'label': '31104.fx.432.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '432.cx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cx1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186245934
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.v1', '216.q1', '216.v1', '216.w1', '216.x1', '216.cr1', '216.fb1', '216.fd1'], 'contains': ['864.m1', '864.o1', '864.be1', '864.bg2', '864.cu1', '864.ei1', '864.fd1', '1296.co1', '1296.cp1', '1296.cq1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [36, 12384, 18576, 72, 12096], 'label': '31104.fx.432.cy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '432.cy1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cy1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186245935
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.v1', '216.cs1', '216.fc1', '216.fd1'], 'contains': ['864.n1', '864.o1', '864.bf1', '864.bg1', '864.cv1', '864.ej1', '864.fe1', '1296.co1', '1296.cq1', '1296.cr1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [36, 12384, 16056, 18144, 12096], 'label': '31104.fx.432.cz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.dw1', 'old_label': '432.cz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cz1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 186245936
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1', '18.t1'], 'contains': ['72.p1', '72.s1', '72.z1', '72.ba1', '72.bf1', '108.by1', '108.ca1', '108.cb1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [16057, 2592, 12096, 16092, 15552, 10368, 22752, 18576], 'label': '31104.fx.36.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '36.t1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.t1', 'subgroup_fusion': None, 'weyl_group': '864.4406'}
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id: 186245937
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.gc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.w1', '216.k1', '216.y1', '216.z1', '216.ba1', '216.bi1', '216.bj1', '216.ct1'], 'contains': ['864.cr1', '864.ek1', '864.fn1', '1296.cs1', '1296.ct1', '1296.cu1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [17371, 18576, 18648, 12096, 10368], 'label': '31104.fx.432.da1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.da1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.da1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
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id: 186245938
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.gc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.w1', '216.l1', '216.bc1', '216.bg1', '216.bh1', '216.bi1', '216.bj1', '216.cv1'], 'contains': ['864.cr1', '864.el1', '864.fo1', '1296.ct1', '1296.cv1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [17371, 22752, 18648, 12096, 18576], 'label': '31104.fx.432.db1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '432.db1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.db1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245939
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.gc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.w1', '216.m1', '216.bd1', '216.cu1'], 'contains': ['864.cs1', '864.em1', '864.fp1', '1296.cu1', '1296.cv1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [17371, 22752, 15552, 12096, 2592], 'label': '31104.fx.432.dc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.g1', 'old_label': '432.dc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dc1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186245940
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.nh1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.w1', '216.n1', '216.bb1', '216.be1', '216.bf1', '216.bk1', '216.bl1', '216.cw1'], 'contains': ['864.ct1', '864.en1', '864.fv1', '1296.cs1', '1296.cv1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [12138, 10368, 18144, 22752, 16056], 'label': '31104.fx.432.dd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '432.dd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dd1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186245941
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ep1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.x1', '216.l1', '216.y1', '216.z1', '216.bc1', '216.bo1', '216.bp1', '216.cy1'], 'contains': ['864.cr1', '864.eo1', '864.fr1', '1296.cw1', '1296.cy1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [6, 12096, 18648, 10368, 18576], 'label': '31104.fx.432.de1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.de1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.de1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245942
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ep1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.x1', '216.m1', '216.bd1', '216.cx1'], 'contains': ['864.cs1', '864.ep1', '864.fs1', '1296.cw1', '1296.cz1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [6, 12096, 18144, 10368, 16056], 'label': '31104.fx.432.df1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.k1', 'old_label': '432.df1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.df1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186245943
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.kw1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.x1', '216.n1', '216.bb1', '216.be1', '216.bf1', '216.bm1', '216.bn1', '216.cz1'], 'contains': ['864.ct1', '864.eq1', '864.fx1', '1296.cw1', '1296.cx1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [6, 22752, 18144, 10368, 16056], 'label': '31104.fx.432.dg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.dg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dg1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186245944
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ep1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.x1', '216.k1', '216.ba1', '216.bg1', '216.bh1', '216.bo1', '216.bp1', '216.da1'], 'contains': ['864.cr1', '864.er1', '864.ft1', '1296.cx1', '1296.cy1', '1296.cz1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [26047, 10368, 18648, 18576, 12096], 'label': '31104.fx.432.dh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '432.dh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dh1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186245945
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.di1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.y1', '216.o1', '216.bb1', '216.bq1', '216.br1', '216.db1', '216.fe1'], 'contains': ['864.p1', '864.ct1', '864.es1', '1296.da1', '1296.db1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [10405, 10368, 15552, 2592, 22752], 'label': '31104.fx.432.di1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '432.di1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.di1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
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id: 186245946
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.y1', '216.p1', '216.y1', '216.bg1', '216.bs1', '216.bu1', '216.dc1', '216.ff1'], 'contains': ['864.q1', '864.cr1', '864.et1', '1296.da1', '1296.dc1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [10405, 1728, 18144, 2592, 10368], 'label': '31104.fx.432.dj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '432.dj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dj1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186245947
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.c1', '18.d1', '18.w1'], 'contains': ['72.z1', '72.bc1', '72.be1', '108.bz1', '108.cc1', '108.cd1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [26485, 15984, 18576, 27690, 18648, 10368, 12096, 22752], 'label': '31104.fx.36.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '36.u1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.u1', 'subgroup_fusion': None, 'weyl_group': '576.7160'}
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id: 186245948
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.y1', '216.q1', '216.bt1', '216.bt2', '216.bv1', '216.dd1', '216.fi1', '216.fj1'], 'contains': ['864.t1', '864.u1', '864.cu1', '864.eu1', '1296.db1', '1296.dc1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [10405, 1728, 18144, 15552, 12384], 'label': '31104.fx.432.dk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '432.dk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dk1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245949
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.z1', '216.bs1', '216.bw1', '216.ca1', '216.cb1', '216.df1', '216.ez1', '216.fr1'], 'contains': ['864.bc1', '864.bh1', '864.bm2', '864.cr1', '864.ev1', '1296.dd1', '1296.df1', '1296.dh1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [18180, 10368, 18648, 18576, 12096], 'label': '31104.fx.432.dl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.be1', 'old_label': '432.dl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dl1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186245950
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.z1', '216.de1', '216.ez1', '216.fr1'], 'contains': ['864.bc1', '864.bc2', '864.bh1', '864.bm1', '864.cs1', '864.ew1', '864.ew2', '1296.dd1', '1296.dg1', '1296.dg2', '1296.dh1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [16092, 22752, 15552, 2592, 12096], 'label': '31104.fx.432.dm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.du1', 'old_label': '432.dm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dm1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 186245951
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.z1', '216.bq1', '216.bz1', '216.cc1', '216.cd1', '216.dg1', '216.fa1', '216.fs1'], 'contains': ['864.bd1', '864.bi1', '864.bn1', '864.ct1', '864.ex1', '1296.dd1', '1296.de1', '1296.de2'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [15588, 10368, 18144, 16056, 22752], 'label': '31104.fx.432.dn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bd1', 'old_label': '432.dn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dn1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
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id: 186245952
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.z1', '216.bt1', '216.by1', '216.ce1', '216.cf1', '216.dh1', '216.fb1', '216.fv1'], 'contains': ['864.be1', '864.bl1', '864.bq1', '864.cu1', '864.ey2', '1296.de1', '1296.df1', '1296.dg1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [18180, 12384, 18648, 72, 12096], 'label': '31104.fx.432.do1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '432.do1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.do1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186245953
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.do2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.z1', '216.bt2', '216.bx1', '216.ce2', '216.cg1', '216.dh1', '216.fd1', '216.ft1'], 'contains': ['864.bg1', '864.bj1', '864.bo1', '864.cu1', '864.ey1', '1296.de2', '1296.df1', '1296.dg2'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [15588, 12384, 18576, 72, 12096], 'label': '31104.fx.432.do2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '432.do2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.do2', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186245954
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.z1', '216.di1', '216.fc1', '216.fv1'], 'contains': ['864.bf1', '864.bl1', '864.bq2', '864.cv1', '864.ez3', '1296.de1', '1296.dg2', '1296.dh1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [18252, 12384, 16056, 18144, 12096], 'label': '31104.fx.432.dp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.dw1', 'old_label': '432.dp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dp1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 186245955
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.dp2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.z1', '216.di1', '216.fd1', '216.fu1'], 'contains': ['864.bg1', '864.bg2', '864.bk1', '864.bp1', '864.cv1', '864.ez1', '864.ez2', '1296.de2', '1296.dg1', '1296.dh1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [540, 12384, 16056, 18144, 12096], 'label': '31104.fx.432.dp2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.dw1', 'old_label': '432.dp2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dp2', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 186245956
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ba1', '216.ba1', '216.bc1', '216.bu1', '216.ch1', '216.ck1', '216.cp1', '216.fr1'], 'contains': ['864.bm1', '864.cr1', '864.ff1', '864.ff2', '1296.di1', '1296.dk1', '1296.dm1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [2628, 10368, 18648, 18576, 12096], 'label': '31104.fx.432.dq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '432.dq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dq1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186245957
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ba1', '216.bd1', '216.co1', '216.fr1'], 'contains': ['864.bm1', '864.bm2', '864.cs1', '864.fg1', '864.fg2', '1296.di1', '1296.dl1', '1296.dm1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [18612, 10368, 18144, 16056, 12096], 'label': '31104.fx.432.dr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bb1', 'old_label': '432.dr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dr1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186245958
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.e1', '18.f1', '18.t1'], 'contains': ['72.r1', '72.t1', '72.ba1', '72.bb1', '72.bd1', '108.ce1', '108.cf1', '108.cg1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1, 2592, 12096, 16092, 15552, 10368, 22752, 18576], 'label': '31104.fx.36.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '36.v1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.v1', 'subgroup_fusion': None, 'weyl_group': '864.4406'}
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id: 186245959
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ba1', '216.be1', '216.br1', '216.cj1', '216.cl1', '216.cq1', '216.fs1'], 'contains': ['864.bn1', '864.ct1', '864.fh1', '1296.di1', '1296.dj1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [468, 10368, 18144, 16056, 22752], 'label': '31104.fx.432.ds1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '432.ds1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ds1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186247006
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1152.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.bz1', '288.ca1', '384.c1'], 'contains': ['3456.m1', '3456.n1', '3456.o1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 384, 'diagramx': None, 'generators': [18868, 29904], 'label': '31104.fx.1152.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '384.c1', 'old_label': '1152.q1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.q1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
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id: 186245960
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ba1', '216.bv1', '216.ci1', '216.cm1', '216.cn1', '216.cr1', '216.ft1', '216.fv1'], 'contains': ['864.bo1', '864.bq2', '864.cu1', '864.fi1', '1296.dj1', '1296.dk1', '1296.dl1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [2628, 12384, 18576, 72, 12096], 'label': '31104.fx.432.dt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '432.dt1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dt1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 186245961
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ba1', '216.cs1', '216.fu1', '216.fv1'], 'contains': ['864.bp1', '864.bq1', '864.bq2', '864.cv1', '864.fj1', '1296.dj1', '1296.dl1', '1296.dm1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [18612, 12384, 16056, 18144, 12096], 'label': '31104.fx.432.du1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.dw1', 'old_label': '432.du1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.du1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 186245962
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.dv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.bb1', '216.p1', '216.bi1', '216.bo1', '216.bw1', '216.ch1', '216.dj1', '216.fw1'], 'contains': ['864.br1', '864.cr1', '864.fk1', '1296.dn1', '1296.do1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1, 10368, 15552, 2592, 1728], 'label': '31104.fx.432.dv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '432.dv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dv1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186245963
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bb1', '216.q1', '216.bx1', '216.by1', '216.ci1', '216.dk1', '216.fx1', '216.fy1'], 'contains': ['864.bs1', '864.bt1', '864.cu1', '864.fl1', '1296.dn1', '1296.dp1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1, 12384, 18144, 15552, 1728], 'label': '31104.fx.432.dw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '432.dw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dw1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245964
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.dx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.dc1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bb1', '216.o1', '216.bk1', '216.bm1', '216.bz1', '216.cj1', '216.dl1', '216.ga1'], 'contains': ['864.bv1', '864.ct1', '864.fm1', '1296.do1', '1296.dp1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1, 10368, 15552, 2592, 22752], 'label': '31104.fx.432.dx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '432.dx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dx1', 'subgroup_fusion': None, 'weyl_group': '144.154'}
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id: 186245965
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.bc1', '216.r1', '216.z1', '216.bh1', '216.ca1', '216.ch1', '216.dc1', '216.ge1'], 'contains': ['864.cr1', '864.fq1', '1296.dq1', '1296.dz1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [10837, 1728, 15552, 10368, 2592], 'label': '31104.fx.432.dy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '432.dy1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dy1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186245966
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.bd1', '216.s1', '216.bw1', '216.cb1', '216.ck1', '216.dp1', '216.ff1', '216.ge1'], 'contains': ['864.bz1', '864.cr1', '1296.dr1', '1296.ea1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [26461, 1728, 2592, 10368, 15552], 'label': '31104.fx.432.dz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '432.dz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dz1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245967
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.be1', '216.r1', '216.bj1', '216.bp1', '216.bu1', '216.cb1', '216.dj1', '216.gf1'], 'contains': ['864.cr1', '864.fu1', '1296.ds1', '1296.eb1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [433, 10368, 15552, 1728, 2592], 'label': '31104.fx.432.ea1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '432.ea1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ea1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186245968
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.eb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.bf1', '216.s1', '216.bs1', '216.ca1', '216.ck1', '216.dt1', '216.fw1', '216.gf1'], 'contains': ['864.ca1', '864.cr1', '1296.dt1', '1296.ec1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [16057, 10368, 2592, 1728, 15552], 'label': '31104.fx.432.eb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.be1', 'old_label': '432.eb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.eb1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245969
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1', '18.f1', '18.z1'], 'contains': ['72.bb1', '72.bc1', '108.ch1', '108.cj1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [5713, 15984, 18576, 27690, 18648, 10368, 22752, 12096], 'label': '31104.fx.36.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '36.w1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.w1', 'subgroup_fusion': None, 'weyl_group': '576.7160'}
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id: 186245970
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ec1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ec1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bc1', '216.t1', '216.bf1', '216.cc1', '216.cj1', '216.db1', '216.gj1'], 'contains': ['864.ct1', '864.fw1', '1296.dq1', '1296.du1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [10837, 2592, 18144, 22752, 10368], 'label': '31104.fx.432.ec1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '432.ec1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ec1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
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id: 186245971
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ed1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ed1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bd1', '216.u1', '216.bz1', '216.cd1', '216.cl1', '216.dv1', '216.fe1', '216.gj1'], 'contains': ['864.ce1', '864.ct1', '1296.dr1', '1296.dv1', '1296.dw1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [26461, 15552, 2592, 22752, 10368], 'label': '31104.fx.432.ed1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bd1', 'old_label': '432.ed1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ed1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186245972
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ee1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.dz1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.be1', '216.t1', '216.bl1', '216.bn1', '216.br1', '216.cd1', '216.dl1', '216.gk1'], 'contains': ['864.ct1', '864.fy1', '1296.ds1', '1296.dx1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [433, 10368, 15552, 2592, 22752], 'label': '31104.fx.432.ee1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '432.ee1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ee1', 'subgroup_fusion': None, 'weyl_group': '144.154'}
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id: 186245973
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ef1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.ea1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bf1', '216.u1', '216.bq1', '216.cc1', '216.cl1', '216.dx1', '216.ga1', '216.gk1'], 'contains': ['864.cf1', '864.ct1', '1296.dt1', '1296.dy1', '1296.dy2'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [16057, 10368, 2592, 15552, 22752], 'label': '31104.fx.432.ef1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '432.ef1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ef1', 'subgroup_fusion': None, 'weyl_group': '72.49'}
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id: 186245974
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.eg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bc1', '216.v1', '216.ce1', '216.ce2', '216.ci1', '216.dd1', '216.gl1', '216.gm1'], 'contains': ['864.cu1', '864.fz1', '1296.du1', '1296.dz1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [28981, 1728, 15552, 12384, 2592], 'label': '31104.fx.432.eg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '432.eg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.eg1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245975
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.eh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bd1', '216.w1', '216.bx1', '216.cf1', '216.cm1', '216.dy1', '216.fj1', '216.gl1'], 'contains': ['864.cg1', '864.cu1', '1296.dv1', '1296.ea1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [26461, 1728, 18144, 12384, 15552], 'label': '31104.fx.432.eh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '432.eh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.eh1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245976
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ei1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bd1', '216.x1', '216.by1', '216.cg1', '216.cn1', '216.dy1', '216.fi1', '216.gm1'], 'contains': ['864.ch1', '864.cu1', '1296.dw1', '1296.ea1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [13069, 1728, 15552, 12384, 18144], 'label': '31104.fx.432.ei1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '432.ei1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ei1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245977
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.be1', '216.v1', '216.bv1', '216.cf1', '216.cg1', '216.dk1', '216.gn1', '216.go1'], 'contains': ['864.cu1', '864.ga1', '1296.dx1', '1296.eb1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [18577, 12384, 15552, 1728, 2592], 'label': '31104.fx.432.ej1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '432.ej1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ej1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245978
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bf1', '216.w1', '216.bt2', '216.ce1', '216.cn1', '216.dz1', '216.fy1', '216.gn1'], 'contains': ['864.ci1', '864.cu1', '1296.dy1', '1296.ec1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [16057, 12384, 18144, 1728, 15552], 'label': '31104.fx.432.ek1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '432.ek1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ek1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245979
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ek2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bf1', '216.x1', '216.bt1', '216.ce2', '216.cm1', '216.dz1', '216.fx1', '216.go1'], 'contains': ['864.cj1', '864.cu1', '1296.dy2', '1296.ec1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [2665, 12384, 15552, 1728, 18144], 'label': '31104.fx.432.ek2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '432.ek2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ek2', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186245980
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1', '18.e1', '18.bm1'], 'contains': ['72.bb1', '72.be1', '108.ci1', '108.ck1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [5713, 18576, 12096, 15558, 15984, 10368, 22752, 18648], 'label': '31104.fx.36.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '36.x1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.x1', 'subgroup_fusion': None, 'weyl_group': '1728.39001'}
-
id: 186245981
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.el1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.bg1', '216.co1', '216.cu1', '216.cx1', '216.de1', '216.dn1', '216.dq1', '216.gw1'], 'contains': ['864.a1', '864.b1', '864.cs1', '864.gb1', '864.gd1', '1296.ed1', '1296.eg1', '1296.eh1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [18144, 10368, 16056, 18576, 12096], 'label': '31104.fx.432.el1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.s1', 'old_label': '432.el1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.el1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186245982
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.em1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.bg1', '216.cp1', '216.ct1', '216.cv1', '216.cy1', '216.da1', '216.dc1', '216.df1', '216.dj1', '216.dm1', '216.do1', '216.dp1', '216.dr1', '216.ds1', '216.dt1', '216.gw1'], 'contains': ['864.a1', '864.cr1', '864.gb1', '864.gc1', '1296.ed1', '1296.ef1', '1296.eg1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [18576, 22752, 18144, 16056, 12096], 'label': '31104.fx.432.em1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '432.em1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.em1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186245983
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.en1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bg1', '216.b1', '216.cq1', '216.cw1', '216.cz1', '216.db1', '216.dg1', '216.dl1', '216.du1', '216.dv1', '216.dw1', '216.dx1'], 'contains': ['864.c1', '864.ct1', '864.gi1', '1296.ed1', '1296.ee1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [18576, 10368, 18144, 16056, 22752], 'label': '31104.fx.432.en1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '432.en1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.en1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186245984
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.eo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bg1', '216.cr1', '216.dd1', '216.dh1', '216.dk1', '216.dy1', '216.dz1', '216.hc1'], 'contains': ['864.e1', '864.g1', '864.cu1', '864.gj1', '1296.ee1', '1296.ef1', '1296.eh1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [2592, 12384, 18576, 72, 12096], 'label': '31104.fx.432.eo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '432.eo1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.eo1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186245985
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ep1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bg1', '216.cs1', '216.di1', '216.hc1'], 'contains': ['864.d1', '864.f1', '864.g1', '864.cv1', '864.gj1', '1296.ee1', '1296.eg1', '1296.eh1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [16056, 12384, 18576, 18144, 12096], 'label': '31104.fx.432.ep1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1', 'old_label': '432.ep1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ep1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186245986
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.eq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.dn1', '144.bh1', '144.bi1', '144.bj1', '216.ea1'], 'contains': ['864.ea1', '1296.ei1', '1296.ej1', '1296.ek1', '1728.s1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [36, 15552, 12460, 16080, 18648], 'label': '31104.fx.432.eq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ea1', 'old_label': '432.eq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.eq1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186245987
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.er1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ck1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.do1', '144.bh1', '144.bl1', '216.eb1'], 'contains': ['864.h1', '864.z1', '864.cx1', '1296.ei1', '1296.el1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [36, 10368, 3096, 15552, 12940], 'label': '31104.fx.432.er1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bg1', 'old_label': '432.er1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.er1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186245988
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.es1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cl1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.bh1', '144.bm1', '216.ec1', '216.ew1'], 'contains': ['864.cy1', '1296.ej1', '1296.el1', '1728.t1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [36, 10368, 12940, 72, 18144], 'label': '31104.fx.432.es1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '432.es1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.es1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186245989
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.et1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.dp1', '144.bh1', '144.bn1', '216.ed1'], 'contains': ['864.cz1', '1296.ek1', '1296.el1', '1728.u1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [36, 10368, 22828, 18648, 15552], 'label': '31104.fx.432.et1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bg1', 'old_label': '432.et1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.et1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186245990
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.eu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.dq1', '144.bh1', '144.bk1', '144.bn1', '216.ee1'], 'contains': ['864.da1', '1296.ek1', '1296.el1', '1728.v1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [36, 22752, 20812, 18648, 15552], 'label': '31104.fx.432.eu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bg1', 'old_label': '432.eu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.eu1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186245991
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1', '18.o1'], 'contains': ['72.bk1', '72.bq1', '72.bt1', '72.by1', '72.ci1', '108.cl1', '108.cm1', '108.cn1', '108.cr1', '144.f1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1, 2016, 10368, 36, 10924, 18144, 72, 2664], 'label': '31104.fx.36.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '36.y1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.y1', 'subgroup_fusion': None, 'weyl_group': '864.4691'}
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id: 186245992
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ev1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ck1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.dr1', '144.bj1', '144.bl1', '216.ef1'], 'contains': ['864.i1', '864.ba1', '864.di1', '1296.ei1', '1296.en1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [36, 2016, 3096, 15552, 10924], 'label': '31104.fx.432.ev1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bi1', 'old_label': '432.ev1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ev1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186245993
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ew1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ck1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.ds1', '144.bi1', '144.bl1', '144.bo1', '216.eg1'], 'contains': ['864.j1', '864.bb1', '864.dj1', '1296.ei1', '1296.em1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [36, 12384, 3096, 15552, 556], 'label': '31104.fx.432.ew1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bh1', 'old_label': '432.ew1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ew1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186245994
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ex1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cl1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bi1', '144.bm1', '216.eh1', '216.ex1'], 'contains': ['864.dk1', '1296.ej1', '1296.em1', '1728.w1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [36, 2016, 10924, 72, 18144], 'label': '31104.fx.432.ex1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1', 'old_label': '432.ex1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ex1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186245995
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ey1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cl1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bj1', '144.bm1', '144.bp1', '216.ei1', '216.ey1'], 'contains': ['864.dl1', '1296.ej1', '1296.en1', '1728.x1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [36, 12384, 556, 72, 18144], 'label': '31104.fx.432.ey1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1', 'old_label': '432.ey1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ey1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186245996
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ez1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.dt1', '144.bi1', '144.bn1', '216.ej1'], 'contains': ['864.dm1', '1296.ek1', '1296.em1', '1728.y1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [36, 12384, 76, 18648, 15552], 'label': '31104.fx.432.ez1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bh1', 'old_label': '432.ez1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ez1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186245997
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.fa1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.dt1', '144.bj1', '144.bn1', '216.ek1'], 'contains': ['864.dn1', '1296.ek1', '1296.en1', '1728.y1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [36, 12384, 76, 72, 18144], 'label': '31104.fx.432.fa1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bi1', 'old_label': '432.fa1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fa1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186245998
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.fb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.bk1', '144.bq1', '216.em1', '216.ez1'], 'contains': ['864.k1', '864.bh1', '864.cw1', '1296.el1', '1296.eo1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [36, 10368, 3096, 15552, 12096], 'label': '31104.fx.432.fb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.q1', 'old_label': '432.fb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fb1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
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id: 186245999
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.fc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.fx1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bl1', '144.bm1', '144.bn1', '144.bq1', '216.el1', '216.fa1'], 'contains': ['864.l1', '864.bi1', '864.df1', '1296.el1', '1296.em1', '1296.en1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [36, 10368, 3096, 15552, 22752], 'label': '31104.fx.432.fc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '432.fc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fc1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
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id: 186246000
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.fd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bo1', '144.bq1', '216.en1', '216.fd1'], 'contains': ['864.m1', '864.n1', '864.bj1', '864.bk1', '864.dg1', '1296.em1', '1296.eo1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [36, 12384, 15552, 18648, 12096], 'label': '31104.fx.432.fd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.r1', 'old_label': '432.fd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fd1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
-
id: 186246001
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.fe1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bp1', '144.bq1', '216.eo1', '216.fb1', '216.fc1'], 'contains': ['864.o1', '864.bl1', '864.dh1', '1296.en1', '1296.eo1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [36, 12384, 18216, 18144, 12096], 'label': '31104.fx.432.fe1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.r1', 'old_label': '432.fe1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fe1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
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id: 186246002
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '3.a1'], 'contains': ['12.c1', '12.j1', '12.o1', '18.g1', '18.h1', '18.l1', '18.n1', '96.o1'], 'core': '12.c1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [19135, 18144, 22752, 10368, 15552, 36, 25852, 18576, 16056, 5712], 'label': '31104.fx.6.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.c1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1', 'subgroup_fusion': None, 'weyl_group': '10368.fj'}
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id: 186246003
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1', '18.r1'], 'contains': ['72.bo1', '72.bs1', '72.bu1', '72.ca1', '72.cg1', '108.cn1', '108.ct1', '144.g1'], 'core': '31104.a1', 'coset_action_label': '36T13454', 'count': 18, 'diagramx': None, 'generators': [20737, 1728, 12384, 36, 556, 18144, 72, 2664], 'label': '31104.fx.36.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.r1', 'old_label': '36.z1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.z1', 'subgroup_fusion': None, 'weyl_group': '864.4000'}
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id: 186246004
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ff1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.br1', '144.bs1', '144.bt1', '144.bu1', '144.bv1', '144.bw1', '144.bx1', '216.el1', '216.ep1', '216.fe1'], 'contains': ['864.p1', '864.ce1', '864.df1', '1296.ep1', '1296.eq1', '1296.er1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [10405, 15552, 3096, 22752, 10368], 'label': '31104.fx.432.ff1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cr1', 'old_label': '432.ff1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ff1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186246005
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.fg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.br1', '144.by1', '216.em1', '216.et1', '216.ff1'], 'contains': ['864.q1', '864.bz1', '864.cw1', '1296.ep1', '1296.es1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [10405, 1728, 3096, 10368, 15552], 'label': '31104.fx.432.fg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bc1', 'old_label': '432.fg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fg1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246006
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.fh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.ez1', '144.bs1', '144.bz1', '216.eb1'], 'contains': ['864.r1', '864.cb1', '864.cx1', '1296.ep1', '1296.et1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [10405, 12940, 3096, 22752, 15552], 'label': '31104.fx.432.fh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bj1', 'old_label': '432.fh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fh1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246007
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.fi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.bt1', '144.bz1', '216.ec1', '216.eq1', '216.fg1'], 'contains': ['864.cy1', '1296.ep1', '1296.eu1', '1728.cf1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [10405, 18144, 10368, 12940, 72], 'label': '31104.fx.432.fi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.y1', 'old_label': '432.fi1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fi1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186246008
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.fj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.fa1', '144.bu1', '144.bz1', '216.ed1'], 'contains': ['864.cz1', '1296.ep1', '1296.ev1', '1728.cg1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [10405, 15552, 22752, 16080, 18648], 'label': '31104.fx.432.fj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bl1', 'old_label': '432.fj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fj1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186246009
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.fk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.fb1', '144.bu1', '144.by1', '144.bz1', '144.ca1', '216.ee1'], 'contains': ['864.da1', '1296.ep1', '1296.ev1', '1728.ch1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [10405, 15552, 10368, 16080, 18648], 'label': '31104.fx.432.fk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bl1', 'old_label': '432.fk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fk1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186246010
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.fl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.fc1', '144.bv1', '144.ca1'], 'contains': ['864.s1', '864.cd1', '864.dc1', '1296.ep1', '1296.ew1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [10405, 29404, 18216, 10368, 18144], 'label': '31104.fx.432.fl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.bv1', 'old_label': '432.fl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fl1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186246011
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.fm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.bw1', '144.ca1', '216.fh1'], 'contains': ['864.dd1', '1296.ep1', '1296.ex1', '1728.ci1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [10405, 15552, 22752, 29404, 3096], 'label': '31104.fx.432.fm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bz1', 'old_label': '432.fm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fm1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186246012
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.fn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.fd1', '144.bx1', '144.by1'], 'contains': ['864.de1', '1296.ep1', '1296.ey1', '1728.cj1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [10405, 15552, 22752, 24268, 18648], 'label': '31104.fx.432.fn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.bx1', 'old_label': '432.fn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fn1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186246013
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.fn2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.fd2', '144.bx1', '144.ca1'], 'contains': ['864.de2', '1296.ep1', '1296.ey1', '1728.cj2'], 'core': '10368.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [10405, 15552, 22752, 9168, 18648], 'label': '31104.fx.432.fn2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.bx1', 'old_label': '432.fn2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fn2', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186246014
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1', '18.o1'], 'contains': ['72.bt1', '72.cl1', '72.cm1', '108.co1', '108.cp1', '108.cq1', '108.cw1', '144.h1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [18577, 2016, 10368, 36, 29068, 18144, 18216, 2592], 'label': '31104.fx.36.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '36.ba1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ba1', 'subgroup_fusion': None, 'weyl_group': '864.4691'}
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id: 186246015
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.fo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.br1', '144.cb1', '216.en1', '216.eu1', '216.fj1'], 'contains': ['864.t1', '864.cg1', '864.dg1', '1296.eq1', '1296.es1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [10405, 1728, 3096, 12384, 15552], 'label': '31104.fx.432.fo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bc1', 'old_label': '432.fo1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fo1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246016
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.fp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.br1', '144.cc1', '216.eo1', '216.ev1', '216.fi1'], 'contains': ['864.u1', '864.ch1', '864.dh1', '1296.er1', '1296.es1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [10405, 1728, 18216, 12384, 18144], 'label': '31104.fx.432.fp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bc1', 'old_label': '432.fp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fp1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246017
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.fq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.ff1', '144.bs1', '144.cg1', '216.ef1'], 'contains': ['864.v1', '864.ck1', '864.di1', '1296.er1', '1296.et1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [10405, 12940, 3096, 2016, 15552], 'label': '31104.fx.432.fq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bj1', 'old_label': '432.fq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fq1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246018
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.fr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.fg1', '144.bs1', '144.cb1', '144.cd1', '144.ce1', '216.eg1'], 'contains': ['864.w1', '864.cm1', '864.dj1', '1296.eq1', '1296.et1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [10405, 12940, 3096, 12384, 15552], 'label': '31104.fx.432.fr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bj1', 'old_label': '432.fr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fr1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246019
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.fs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bt1', '144.ce1', '216.eh1', '216.er1', '216.fk1'], 'contains': ['864.dk1', '1296.eq1', '1296.eu1', '1728.cl1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [10405, 18144, 2016, 12940, 72], 'label': '31104.fx.432.fs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.y1', 'old_label': '432.fs1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fs1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186246020
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ft1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bt1', '144.cc1', '144.cf1', '144.cg1', '216.ei1', '216.es1', '216.fl1'], 'contains': ['864.dl1', '1296.er1', '1296.eu1', '1728.cm1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [10405, 18144, 12384, 12940, 72], 'label': '31104.fx.432.ft1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.y1', 'old_label': '432.ft1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ft1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
-
id: 186246021
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.fu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.fh1', '144.bu1', '144.ce1', '216.ej1'], 'contains': ['864.dm1', '1296.eq1', '1296.ev1', '1728.cn1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [10405, 15552, 12384, 16080, 18648], 'label': '31104.fx.432.fu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bl1', 'old_label': '432.fu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fu1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186246022
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.fv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.fh1', '144.bu1', '144.cg1', '216.ek1'], 'contains': ['864.dn1', '1296.er1', '1296.ev1', '1728.cn1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [10405, 18144, 12384, 12460, 18216], 'label': '31104.fx.432.fv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bl1', 'old_label': '432.fv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fv1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186246023
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.fw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.fi1', '144.bv1', '144.cb1'], 'contains': ['864.x1', '864.cp1', '864.dq1', '1296.eq1', '1296.ew1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [10405, 29404, 18216, 2016, 18144], 'label': '31104.fx.432.fw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.bv1', 'old_label': '432.fw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fw1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186246024
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.fx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.fi2', '144.bv1', '144.cf1'], 'contains': ['864.y1', '864.cq1', '864.dr1', '1296.er1', '1296.ew1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [10405, 29404, 18216, 12384, 18144], 'label': '31104.fx.432.fx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.bv1', 'old_label': '432.fx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fx1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186246025
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1', '18.r1'], 'contains': ['72.bu1', '72.co1', '72.cp1', '108.cq1', '108.cx1', '144.i1'], 'core': '31104.a1', 'coset_action_label': '36T13456', 'count': 18, 'diagramx': None, 'generators': [8209, 1728, 12384, 36, 18700, 18144, 18216, 2592], 'label': '31104.fx.36.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.r1', 'old_label': '36.bb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bb1', 'subgroup_fusion': None, 'weyl_group': '864.4000'}
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id: 186246026
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.fy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bw1', '144.cd1', '216.fn1'], 'contains': ['864.ds1', '1296.eq1', '1296.ex1', '1728.co1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [10405, 15552, 12384, 29404, 3096], 'label': '31104.fx.432.fy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bz1', 'old_label': '432.fy1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fy1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186246027
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.fz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bw1', '144.cc1', '216.fm1'], 'contains': ['864.dt1', '1296.er1', '1296.ex1', '1728.co2'], 'core': '31104.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [10405, 15552, 2016, 29404, 3096], 'label': '31104.fx.432.fz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bz1', 'old_label': '432.fz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fz1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186246028
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ga1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.fj1', '144.bx1', '144.cd1'], 'contains': ['864.du1', '1296.eq1', '1296.ey1', '1728.cp1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [10405, 15552, 12384, 24268, 18648], 'label': '31104.fx.432.ga1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.bx1', 'old_label': '432.ga1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ga1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186246029
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.gb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.fj1', '144.bx1', '144.cf1'], 'contains': ['864.dv1', '1296.er1', '1296.ey1', '1728.cp1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [10405, 18144, 12384, 24268, 18216], 'label': '31104.fx.432.gb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.bx1', 'old_label': '432.gb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gb1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186246030
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.gc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.fk1', '144.bz1', '144.ce1', '144.cg1', '216.ea1'], 'contains': ['864.ea1', '1296.et1', '1296.eu1', '1296.ev1', '1728.cq1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [10405, 15552, 12460, 16080, 18648], 'label': '31104.fx.432.gc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1', 'old_label': '432.gc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gc1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
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id: 186246031
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.gd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ch1', '216.eq1', '216.ew1', '216.fo1'], 'contains': ['864.cy1', '1296.ez1', '1296.fa1', '1728.cr1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [468, 10368, 12940, 72, 18144], 'label': '31104.fx.432.gd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.u1', 'old_label': '432.gd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gd1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186246032
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ge1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ch1', '216.er1', '216.ex1', '216.fp1'], 'contains': ['864.dk1', '1296.ez1', '1296.fb1', '1728.cs1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [468, 2016, 10924, 72, 18144], 'label': '31104.fx.432.ge1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '432.ge1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ge1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186246033
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.gf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ch1', '144.ci1', '144.ci2', '216.es1', '216.ey1', '216.fq1'], 'contains': ['864.dl1', '1296.ez1', '1296.fc1', '1728.ct1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [468, 12384, 556, 72, 18144], 'label': '31104.fx.432.gf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.y1', 'old_label': '432.gf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gf1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186246034
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.gg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.cj1', '216.et1', '216.ez1', '216.fr1'], 'contains': ['864.bc1', '864.bc2', '864.bm1', '864.bm2', '864.cw1', '1296.fa1', '1296.fd1', '1296.fd2'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [3060, 10368, 3096, 15552, 12096], 'label': '31104.fx.432.gg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.be1', 'old_label': '432.gg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gg1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246035
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.gh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ch1', '144.cj1', '216.ep1', '216.fa1', '216.fs1'], 'contains': ['864.bd1', '864.bn1', '864.df1', '1296.fa1', '1296.fb1', '1296.fc1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [3060, 10368, 3096, 15552, 22752], 'label': '31104.fx.432.gh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '432.gh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gh1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
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id: 186246036
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1', '18.t1'], 'contains': ['72.c1', '72.d1', '72.f1', '72.h1', '72.p1', '72.r1', '72.bp1', '72.br1', '72.bw1', '72.bx1', '72.cf1', '108.cr1', '108.cs1', '108.ct1', '108.cu1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1, 15552, 12096, 36, 2592, 10368, 22752, 16056], 'label': '31104.fx.36.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '36.bc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bc1', 'subgroup_fusion': None, 'weyl_group': '432.768'}
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id: 186246037
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.gi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cj1', '216.eu1', '216.fd1', '216.fv1'], 'contains': ['864.be1', '864.bf1', '864.bo1', '864.bp1', '864.dg1', '1296.fb1', '1296.fd1', '1296.fd2'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [108, 12384, 15552, 18648, 12096], 'label': '31104.fx.432.gi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '432.gi1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gi1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246038
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.gj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ci1', '144.cj1', '216.ev1', '216.fb1', '216.fu1'], 'contains': ['864.bg2', '864.bq1', '864.dh1', '1296.fc1', '1296.fd1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [18612, 12384, 18216, 18144, 12096], 'label': '31104.fx.432.gj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.r1', 'old_label': '432.gj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gj1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
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id: 186246039
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.gj2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ci2', '144.cj1', '216.fc1', '216.ft1', '216.fu1'], 'contains': ['864.bg1', '864.bq2', '864.dh1', '1296.fc1', '1296.fd2'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [3060, 12384, 18216, 18144, 12096], 'label': '31104.fx.432.gj2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bp1', 'old_label': '432.gj2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gj2', 'subgroup_fusion': None, 'weyl_group': '54.5'}
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id: 186246040
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.gk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ck1', '144.cl1', '144.cm1', '216.em1', '216.et1', '216.fw1'], 'contains': ['864.br1', '864.ca1', '864.cw1', '1296.fe1', '1296.ff1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1, 10368, 3096, 1728, 15552], 'label': '31104.fx.432.gk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cs1', 'old_label': '432.gk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gk1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246041
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.gl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cm1', '144.cn1', '144.cp1', '216.en1', '216.eu1', '216.fy1'], 'contains': ['864.bs1', '864.ci1', '864.dg1', '1296.fe1', '1296.fg1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1, 12384, 3096, 1728, 15552], 'label': '31104.fx.432.gl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cu1', 'old_label': '432.gl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gl1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246042
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.gm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cm1', '144.co1', '144.cq1', '216.eo1', '216.ev1', '216.fx1'], 'contains': ['864.bt1', '864.cj1', '864.dh1', '1296.fe1', '1296.fh1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1, 12384, 18216, 1728, 18144], 'label': '31104.fx.432.gm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ct1', 'old_label': '432.gm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gm1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246043
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.gn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.fn1', '144.cr1', '144.cs1', '144.ct1', '216.eb1'], 'contains': ['864.bu1', '864.cc1', '864.cx1', '1296.ff1', '1296.fi1', '1296.fl1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [1, 10368, 3096, 15552, 10924], 'label': '31104.fx.432.gn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.eb1', 'old_label': '432.gn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gn1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186246044
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.go1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.cr1', '144.cs1', '144.cu1', '216.ec1', '216.eq1', '216.fz1'], 'contains': ['864.cy1', '1296.ff1', '1296.fj1', '1296.fm1', '1728.dc1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1, 18144, 10924, 10368, 72], 'label': '31104.fx.432.go1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cl1', 'old_label': '432.go1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.go1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186246045
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.gp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.fo1', '144.cr1', '144.cs1', '144.cv1', '216.ed1'], 'contains': ['864.cz1', '1296.ff1', '1296.fk1', '1296.fn1', '1728.dd1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [1, 15552, 5712, 22752, 18648], 'label': '31104.fx.432.gp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ed1', 'old_label': '432.gp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gp1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186246046
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.gq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.fp1', '144.ck1', '144.cs1', '144.cv1', '216.ee1'], 'contains': ['864.da1', '1296.ff1', '1296.fk1', '1728.de1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [1, 15552, 5712, 10368, 18648], 'label': '31104.fx.432.gq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bm1', 'old_label': '432.gq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gq1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
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id: 186246047
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1', '18.t1'], 'contains': ['72.g1', '72.h1', '72.s1', '72.t1', '72.bw1', '72.cj1', '72.ck1', '108.cv1', '108.cw1', '108.cx1', '108.cy1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [433, 2592, 12096, 36, 15552, 10368, 22752, 16056], 'label': '31104.fx.36.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '36.bd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bd1', 'subgroup_fusion': None, 'weyl_group': '432.768'}
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id: 186246048
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.gr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.fq1', '144.cl1', '144.cr1', '144.cv1'], 'contains': ['864.db1', '1296.ff1', '1296.fn1', '1728.df1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [1, 15552, 76, 22752, 18648], 'label': '31104.fx.432.gr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.cl1', 'old_label': '432.gr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gr1', 'subgroup_fusion': None, 'weyl_group': '216.92'}
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id: 186246049
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.gs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cm1', '144.ct1', '144.cu1', '144.cv1', '216.el1', '216.ep1', '216.ga1'], 'contains': ['864.bv1', '864.cf1', '864.df1', '1296.ff1', '1296.fg1', '1296.fh1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1, 10368, 3096, 15552, 22752], 'label': '31104.fx.432.gs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bc1', 'old_label': '432.gs1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gs1', 'subgroup_fusion': None, 'weyl_group': '72.49'}
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id: 186246050
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.gt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.fs1', '144.ct1', '144.cw1', '144.cz1', '216.ef1'], 'contains': ['864.bw1', '864.cl1', '864.di1', '1296.fh1', '1296.fi1', '1296.fl1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1, 2016, 3096, 15552, 10924], 'label': '31104.fx.432.gt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ef1', 'old_label': '432.gt1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gt1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186246051
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.gu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.ft1', '144.cn1', '144.ct1', '144.cy1', '216.eg1'], 'contains': ['864.bx1', '864.cn1', '864.dj1', '1296.fg1', '1296.fi1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [1, 12384, 3096, 15552, 556], 'label': '31104.fx.432.gu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bn1', 'old_label': '432.gu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gu1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
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id: 186246052
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.gv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cu1', '144.cx1', '144.cy1', '216.eh1', '216.er1', '216.gb1'], 'contains': ['864.dk1', '1296.fg1', '1296.fj1', '1296.fm1', '1728.dh1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1, 18144, 10924, 2016, 72], 'label': '31104.fx.432.gv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cm1', 'old_label': '432.gv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gv1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186246053
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.gw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.co1', '144.cu1', '144.cz1', '216.ei1', '216.es1', '216.gc1'], 'contains': ['864.dl1', '1296.fh1', '1296.fj1', '1728.di1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1, 18144, 556, 12384, 72], 'label': '31104.fx.432.gw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.z1', 'old_label': '432.gw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gw1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
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id: 186246054
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.gx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.fu1', '144.cv1', '144.cx1', '144.cy1', '216.ej1'], 'contains': ['864.dm1', '1296.fg1', '1296.fk1', '1296.fn1', '1728.dj1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [1, 15552, 5712, 12384, 18648], 'label': '31104.fx.432.gx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ej1', 'old_label': '432.gx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gx1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186246055
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.gy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.fu1', '144.cv1', '144.cw1', '144.cz1', '216.ek1'], 'contains': ['864.dn1', '1296.fh1', '1296.fk1', '1296.fn1', '1728.dj1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [1, 18144, 76, 12384, 18216], 'label': '31104.fx.432.gy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ek1', 'old_label': '432.gy1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gy1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186246056
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.gz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.fv1', '144.cp1', '144.ct1', '144.cx1'], 'contains': ['864.by1', '864.co1', '864.do1', '1296.fg1', '1296.fl1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [1, 12384, 3096, 15552, 10924], 'label': '31104.fx.432.gz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.cp1', 'old_label': '432.gz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gz1', 'subgroup_fusion': None, 'weyl_group': '108.25'}
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id: 186246057
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ha1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cq1', '144.cu1', '144.cw1', '216.gd1'], 'contains': ['864.dp1', '1296.fh1', '1296.fm1', '1728.dk1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [1, 18144, 10924, 12384, 72], 'label': '31104.fx.432.ha1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.ch1', 'old_label': '432.ha1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ha1', 'subgroup_fusion': None, 'weyl_group': '216.92'}
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id: 186246058
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1', '18.o1'], 'contains': ['72.by1', '72.cb1', '72.cm1', '108.cz1', '108.da1', '108.db1', '108.dc1', '144.l1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [18577, 2016, 10368, 18612, 29068, 18144, 18216, 2592], 'label': '31104.fx.36.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '36.be1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.be1', 'subgroup_fusion': None, 'weyl_group': '864.4691'}
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id: 186246059
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.hb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.fw1', '144.cr1', '144.cs1', '144.cw1', '144.cy1'], 'contains': ['864.dw1', '1296.fi1', '1296.fk1', '1296.fm1', '1296.fn1', '1728.dl1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [1, 15552, 12460, 28464, 18648], 'label': '31104.fx.432.hb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.hb1', 'old_label': '432.hb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hb1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
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id: 186246060
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.hc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.fx1', '144.cr1', '144.cw1', '144.cy1'], 'contains': ['864.dx1', '1296.fi1', '1296.fm1', '1296.fn1', '1728.dm1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [1, 18144, 2524, 28464, 18216], 'label': '31104.fx.432.hc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.hc1', 'old_label': '432.hc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hc1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
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id: 186246061
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.hd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.fw1', '144.cr1', '144.cs1', '144.cx1', '144.cz1'], 'contains': ['864.dy1', '1296.fj1', '1296.fk1', '1296.fl1', '1296.fn1', '1728.dl1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [1, 15552, 22828, 5712, 18648], 'label': '31104.fx.432.hd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.hd1', 'old_label': '432.hd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hd1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
-
id: 186246062
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.he1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.fx1', '144.cr1', '144.cx1', '144.cz1'], 'contains': ['864.dz1', '1296.fj1', '1296.fl1', '1296.fn1', '1728.dm1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [1, 15552, 2092, 28464, 18648], 'label': '31104.fx.432.he1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.he1', 'old_label': '432.he1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.he1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
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id: 186246063
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.hf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.fy1', '144.cs1', '144.cy1', '144.cz1', '216.ea1'], 'contains': ['864.ea1', '1296.fi1', '1296.fj1', '1296.fk1', '1728.dn1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1, 15552, 20812, 5712, 18648], 'label': '31104.fx.432.hf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ea1', 'old_label': '432.hf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hf1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
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id: 186246064
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.hg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.fz1', '144.cr1', '144.cy1', '144.cz1'], 'contains': ['864.eb1', '1296.fi1', '1296.fj1', '1296.fn1', '1728.do1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [1, 15552, 76, 28464, 18648], 'label': '31104.fx.432.hg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.hg1', 'old_label': '432.hg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hg1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
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id: 186246065
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.hh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.ga1', '144.cr1', '144.cs1', '144.cw1', '144.cx1'], 'contains': ['864.ec1', '1296.fk1', '1296.fl1', '1296.fm1', '1296.fn1', '1728.dp1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [1, 15552, 20812, 28464, 18648], 'label': '31104.fx.432.hh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.hh1', 'old_label': '432.hh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hh1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
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id: 186246066
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.hi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.gb1', '144.cs1', '144.cw1', '144.cx1'], 'contains': ['864.ed1', '1296.fk1', '1296.fl1', '1296.fm1', '1728.dq1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [1, 15552, 12460, 5712, 18648], 'label': '31104.fx.432.hi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.hi1', 'old_label': '432.hi1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hi1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
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id: 186246067
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.hj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.gc1', '144.cr1', '144.cw1', '144.cx1'], 'contains': ['864.ee2', '1296.fl1', '1296.fm1', '1296.fn1', '1728.dr1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [1, 15552, 22828, 28464, 18648], 'label': '31104.fx.432.hj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.hj1', 'old_label': '432.hj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hj1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
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id: 186246068
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.hj2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.gc2', '144.cr1', '144.cw1', '144.cx1'], 'contains': ['864.ee1', '1296.fl1', '1296.fm1', '1296.fn1', '1728.dr2'], 'core': '31104.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [1, 15552, 10444, 28464, 18648], 'label': '31104.fx.432.hj2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.hj2', 'old_label': '432.hj2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hj2', 'subgroup_fusion': None, 'weyl_group': '72.43'}
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id: 186246069
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1', '18.t1'], 'contains': ['72.p1', '72.q1', '72.t1', '72.v1', '72.bx1', '72.ce1', '72.ck1', '108.cz1', '108.dd1', '108.de1', '108.df1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [433, 2592, 12096, 468, 15552, 10368, 22752, 16056], 'label': '31104.fx.36.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '36.bf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bf1', 'subgroup_fusion': None, 'weyl_group': '432.768'}
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id: 186246070
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.hk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.da1', '216.ez1', '216.ff1', '216.fr1', '216.fw1', '216.ge1', '216.gf1', '216.gw1'], 'contains': ['864.a1', '864.b1', '864.cr1', '864.cs1', '864.cw1', '1296.fo1', '1296.fr1', '1296.fs1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [16056, 10368, 18144, 15552, 12096], 'label': '31104.fx.432.hk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '432.hk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hk1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186246071
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.hl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.df1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.db1', '216.ew1', '216.fg1', '216.fo1', '216.fz1', '216.gg1', '216.gh1', '216.gx1'], 'contains': ['864.cy1', '1296.fo1', '1296.ft1', '1296.fu1', '1728.b1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [16056, 18144, 10924, 22752, 72], 'label': '31104.fx.432.hl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '432.hl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hl1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186246072
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.hm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.df1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dc1', '216.fh1', '216.gi1', '216.ha1'], 'contains': ['864.dd1', '1296.fo1', '1296.fv1', '1296.fw1', '1728.c1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [18144, 15552, 15868, 29404, 18648], 'label': '31104.fx.432.hm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cp1', 'old_label': '432.hm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hm1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186246073
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.hn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.da1', '144.db1', '144.dc1', '216.b1', '216.fa1', '216.fe1', '216.fs1', '216.ga1', '216.gj1', '216.gk1'], 'contains': ['864.c1', '864.ct1', '864.df1', '1296.fo1', '1296.fp1', '1296.fq1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [18144, 2016, 3096, 15552, 10368], 'label': '31104.fx.432.hn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '432.hn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hn1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186246074
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ho1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.da1', '144.dd1', '144.df1', '216.fb1', '216.fi1', '216.ft1', '216.fx1', '216.gl1', '216.gn1', '216.hc1'], 'contains': ['864.f1', '864.cu1', '864.dh1', '1296.fp1', '1296.fr1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [504, 12384, 18216, 18144, 12096], 'label': '31104.fx.432.ho1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '432.ho1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ho1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186246075
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.hp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.da1', '144.de1', '144.dg1', '216.fc1', '216.fu1', '216.hc1'], 'contains': ['864.g1', '864.cv1', '864.dh1', '1296.fp1', '1296.fs1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [16056, 12384, 18216, 18144, 12096], 'label': '31104.fx.432.hp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.k1', 'old_label': '432.hp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hp1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
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id: 186246076
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.hq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.da1', '216.fd1', '216.fj1', '216.fv1', '216.fy1', '216.gm1', '216.go1', '216.hc1'], 'contains': ['864.d1', '864.e1', '864.cu1', '864.cv1', '864.dg1', '1296.fq1', '1296.fr1', '1296.fs1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [15552, 12384, 504, 18144, 12096], 'label': '31104.fx.432.hq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '432.hq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hq1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186246077
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.hr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.df1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.db1', '216.ex1', '216.fk1', '216.fp1', '216.gb1', '216.gp1', '216.gq1', '216.hd1'], 'contains': ['864.dk1', '1296.fq1', '1296.ft1', '1296.fu1', '1728.h1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [16056, 18144, 10924, 2016, 72], 'label': '31104.fx.432.hr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '432.hr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hr1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186246078
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.hs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.df1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.db1', '144.dd1', '144.de1', '216.ey1', '216.fl1', '216.fq1', '216.gc1', '216.gr1', '216.gs1', '216.he1'], 'contains': ['864.dl1', '1296.fp1', '1296.ft1', '1728.i1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [3024, 18144, 556, 12384, 18216], 'label': '31104.fx.432.hs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '432.hs1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hs1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186246079
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ht1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.df1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.db1', '144.df1', '144.dg1', '216.gd1', '216.gt1', '216.hg1'], 'contains': ['864.dp1', '1296.fp1', '1296.fu1', '1728.j1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [16056, 18144, 10924, 12384, 72], 'label': '31104.fx.432.ht1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.v1', 'old_label': '432.ht1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ht1', 'subgroup_fusion': None, 'weyl_group': '72.42'}
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id: 186246080
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1', '18.r1'], 'contains': ['72.ca1', '72.cc1', '72.cp1', '108.dc1', '108.de1', '144.p1'], 'core': '31104.a1', 'coset_action_label': '36T13453', 'count': 18, 'diagramx': None, 'generators': [8209, 1728, 12384, 18612, 18700, 18144, 18216, 2592], 'label': '31104.fx.36.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.r1', 'old_label': '36.bg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bg1', 'subgroup_fusion': None, 'weyl_group': '864.4000'}
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id: 186246081
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.hu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.df1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dc1', '144.dd1', '144.dg1', '216.fm1', '216.gu1', '216.hh1'], 'contains': ['864.dt1', '1296.fp1', '1296.fv1', '1728.k1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [16056, 15552, 26236, 2016, 18648], 'label': '31104.fx.432.hu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.q1', 'old_label': '432.hu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hu1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
-
id: 186246082
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.hv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.df1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dc1', '144.de1', '144.df1', '144.dg1', '216.hh1'], 'contains': ['864.dt1', '1296.fp1', '1296.fw1', '1728.l1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [18576, 15552, 26236, 2016, 18648], 'label': '31104.fx.432.hv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.n1', 'old_label': '432.hv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hv1', 'subgroup_fusion': None, 'weyl_group': '36.11'}
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id: 186246083
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.hw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.df1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dc1', '216.fn1', '216.gv1', '216.hh2'], 'contains': ['864.ds1', '1296.fq1', '1296.fv1', '1296.fw1', '1728.m1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [18144, 15552, 5500, 29404, 18648], 'label': '31104.fx.432.hw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cp1', 'old_label': '432.hw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hw1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186246084
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.hx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.co1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dh1', '216.k1', '216.hq1', '216.hr1', '216.hw1', '216.hx1', '216.jx1', '216.jy1'], 'contains': ['864.ef1', '864.ek1', '864.er1', '864.gy1', '864.hh1', '1296.fx1', '1296.fy1', '1296.fz1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26047, 10368, 36, 18576, 12096], 'label': '31104.fx.432.hx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.hx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hx1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186246085
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.hy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cn1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dh1', '216.l1', '216.ht1', '216.hu1', '216.hw1', '216.hx1', '216.jz1', '216.kc1'], 'contains': ['864.ef1', '864.el1', '864.eo1', '864.gz1', '864.hl1', '1296.fy1', '1296.ga1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26047, 22752, 36, 18576, 12096], 'label': '31104.fx.432.hy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.hy1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hy1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186246086
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.hz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dh1', '216.m1', '216.ka1', '216.kc1'], 'contains': ['864.eg1', '864.em1', '864.ep1', '864.gz1', '864.hl2', '1296.fz1', '1296.ga1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [6, 10368, 36, 16056, 12096], 'label': '31104.fx.432.hz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.k1', 'old_label': '432.hz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hz1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186246087
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ia1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cr1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dh1', '216.n1', '216.hs1', '216.hv1', '216.hy1', '216.hz1', '216.kb1', '216.kd1'], 'contains': ['864.eh1', '864.en1', '864.eq1', '864.ha1', '864.hm1', '1296.fx1', '1296.ga1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [19135, 10368, 36, 18576, 22752], 'label': '31104.fx.432.ia1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.ia1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ia1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186246088
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ib1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.di1', '216.o1', '216.hs1', '216.hy1', '216.ia1', '216.ke1'], 'contains': ['864.eh1', '864.es1', '864.fm1', '864.hb1', '864.ih1', '1296.gb1', '1296.gc1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1, 10368, 36, 2592, 22752], 'label': '31104.fx.432.ib1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.ib1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ib1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186246089
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ic1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.di1', '216.p1', '216.hq1', '216.ht1', '216.hw1', '216.ib1', '216.kf1', '216.kg1'], 'contains': ['864.ef1', '864.et1', '864.fk1', '864.hc1', '864.in1', '1296.gb1', '1296.gd1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [20737, 22752, 36, 2592, 1728], 'label': '31104.fx.432.ic1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.ic1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ic1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186246090
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.id1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.di1', '216.q1', '216.kh1'], 'contains': ['864.ei1', '864.eu1', '864.fl1', '864.hd1', '864.io1', '1296.gc1', '1296.gd1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [20737, 12384, 36, 2592, 1728], 'label': '31104.fx.432.id1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.p1', 'old_label': '432.id1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.id1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186246091
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1', '18.r1'], 'contains': ['72.cc1', '72.cg1', '72.co1', '108.di1', '108.dk1', '144.q1'], 'core': '31104.a1', 'coset_action_label': '36T13455', 'count': 18, 'diagramx': None, 'generators': [20737, 1728, 12384, 18612, 556, 18144, 18216, 2592], 'label': '31104.fx.36.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.r1', 'old_label': '36.bh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bh1', 'subgroup_fusion': None, 'weyl_group': '864.4000'}
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id: 186246092
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ie1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cu1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dj1', '216.k1', '216.ht1', '216.hu1', '216.ib1', '216.ic1', '216.jx1', '216.ki1'], 'contains': ['864.ef1', '864.fn1', '864.ft1', '1296.ge1', '1296.gi1', '1296.gj1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [10855, 10368, 36, 18576, 12096], 'label': '31104.fx.432.ie1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.ie1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ie1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186246093
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.if1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cn1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dj1', '216.l1', '216.hq1', '216.hr1', '216.ib1', '216.ic1', '216.jz1', '216.kj1'], 'contains': ['864.ef1', '864.fo1', '864.fr1', '1296.gf1', '1296.gi1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [28567, 22752, 36, 18576, 12096], 'label': '31104.fx.432.if1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.if1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.if1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186246094
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ig1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dj1', '216.m1', '216.ka1', '216.kk1'], 'contains': ['864.eg1', '864.fp1', '864.fs1', '1296.gf1', '1296.gj1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [18150, 10368, 36, 16056, 12096], 'label': '31104.fx.432.ig1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.k1', 'old_label': '432.ig1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ig1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186246095
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ih1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dk1', '216.r1', '216.hr1', '216.hu1', '216.hx1', '216.ic1', '216.kf1', '216.kg1'], 'contains': ['864.ef1', '864.fq1', '864.fu1', '1296.gg1', '1296.gk1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5617, 22752, 36, 2592, 1728], 'label': '31104.fx.432.ih1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.ih1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ih1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186246096
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ii1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cr1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dj1', '216.n1', '216.hs1', '216.hv1', '216.ia1', '216.id1', '216.kb1', '216.kl1'], 'contains': ['864.eh1', '864.fv1', '864.fx1', '1296.ge1', '1296.gf1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [3943, 10368, 36, 18576, 22752], 'label': '31104.fx.432.ii1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.ii1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ii1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186246097
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ij1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dk1', '216.t1', '216.hv1', '216.hz1', '216.id1', '216.ke1'], 'contains': ['864.eh1', '864.fw1', '864.fy1', '1296.gg1', '1296.gh1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [15985, 10368, 36, 2592, 22752], 'label': '31104.fx.432.ij1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.ij1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ij1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186246099
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.il1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cy1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dl1', '216.y1', '216.hw1', '216.ie1', '216.ig1', '216.iw1', '216.km1', '216.kq1'], 'contains': ['864.ek1', '864.eo1', '864.et1', '864.he1', '1296.gl1', '1296.gn1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26485, 12096, 12138, 18576, 22752], 'label': '31104.fx.432.il1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.il1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.il1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246100
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.im1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cy1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dn1', '216.z1', '216.hx1', '216.if1', '216.ih1', '216.ix1', '216.km1', '216.kq1'], 'contains': ['864.ek1', '864.eo1', '864.fq1', '1296.gm1', '1296.gr1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [29077, 12096, 12138, 22752, 18576], 'label': '31104.fx.432.im1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.im1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.im1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246101
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.in1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.co1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dm1', '216.ba1', '216.ig1', '216.ih1', '216.iy1', '216.iz1', '216.jy1', '216.kn1'], 'contains': ['864.ek1', '864.er1', '864.ff2', '864.hh1', '1296.go1', '1296.gp1', '1296.gq1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26047, 10368, 2628, 18576, 12096], 'label': '31104.fx.432.in1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.in1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.in1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186246102
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1', '18.o1'], 'contains': ['72.cb1', '72.ci1', '72.cl1', '108.dg1', '108.dh1', '108.di1', '108.dm1', '144.r1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1, 2016, 10368, 18612, 10924, 18144, 18216, 2592], 'label': '31104.fx.36.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '36.bi1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bi1', 'subgroup_fusion': None, 'weyl_group': '864.4691'}
-
id: 186246103
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.io1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cy1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.do1', '216.y1', '216.hq1', '216.ii1', '216.iy1', '216.ja1', '216.ko1', '216.kq1'], 'contains': ['864.ek1', '864.et1', '864.fr1', '1296.gs1', '1296.gt1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26485, 12096, 14802, 22752, 18576], 'label': '31104.fx.432.io1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.io1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.io1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 186246104
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ip1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dp1', '216.k1', '216.ie1', '216.if1', '216.ja1', '216.jb1', '216.kn1', '216.kt1'], 'contains': ['864.ek1', '864.fa1', '864.ft1', '1296.gu1', '1296.gv1', '1296.gw1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [10855, 10368, 18684, 18576, 12096], 'label': '31104.fx.432.ip1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.ip1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ip1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186246105
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.iq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dq1', '216.ba1', '216.ii1', '216.ij1', '216.iw1', '216.ix1', '216.jx1', '216.kt1'], 'contains': ['864.ek1', '864.ff1', '864.ft1', '1296.gx1', '1296.gy1', '1296.gz1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [10855, 10368, 16092, 18576, 12096], 'label': '31104.fx.432.iq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.iq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.iq1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186246106
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ir1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cz1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dr1', '216.bi1', '216.hq1', '216.ie1', '216.ih1', '216.ij1', '216.kp1', '216.le1'], 'contains': ['864.ek1', '864.fk1', '864.fo1', '1296.ha1', '1296.hb1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 10368, 14730, 12096, 18576], 'label': '31104.fx.432.ir1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.ir1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ir1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246107
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.is1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cz1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ds1', '216.bj1', '216.hr1', '216.if1', '216.ig1', '216.ii1', '216.kp1', '216.le1'], 'contains': ['864.ek1', '864.fo1', '864.fu1', '1296.hc1', '1296.he1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [8305, 10368, 14730, 12096, 18576], 'label': '31104.fx.432.is1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.is1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.is1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246108
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.it1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cy1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dt1', '216.z1', '216.hr1', '216.ij1', '216.iz1', '216.jb1', '216.ko1', '216.kq1'], 'contains': ['864.ek1', '864.fq1', '864.fr1', '1296.hd1', '1296.hf1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [29077, 12096, 14802, 22752, 18576], 'label': '31104.fx.432.it1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.it1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.it1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246109
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.iu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.dg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dl1', '216.bb1', '216.hy1', '216.ik1', '216.im1', '216.jc1', '216.ky1', '216.lf1'], 'contains': ['864.en1', '864.eq1', '864.es1', '864.hj1', '1296.gl1', '1296.hj1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26485, 10368, 12138, 18576, 22752], 'label': '31104.fx.432.iu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.iu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.iu1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246110
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.iv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dm1', '216.bc1', '216.iq1', '216.ir1', '216.iw1', '216.ix1', '216.kc1', '216.kv1'], 'contains': ['864.el1', '864.eo1', '864.ff1', '864.hl2', '1296.gp1', '1296.hi1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26047, 22752, 2628, 18576, 12096], 'label': '31104.fx.432.iv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.iv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.iv1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186246111
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.iw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dm1', '216.bd1', '216.kc1', '216.kw1'], 'contains': ['864.em1', '864.ep1', '864.fg2', '864.hl1', '864.hl2', '1296.gq1', '1296.hi1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [6, 10368, 18612, 16056, 12096], 'label': '31104.fx.432.iw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.k1', 'old_label': '432.iw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.iw1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186246112
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ix1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dm1', '216.be1', '216.im1', '216.in1', '216.jc1', '216.jd1', '216.kd1', '216.kx1'], 'contains': ['864.en1', '864.eq1', '864.fh1', '864.hm1', '1296.go1', '1296.hi1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [19135, 10368, 2628, 18576, 22752], 'label': '31104.fx.432.ix1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.ix1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ix1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186246113
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '3.a1'], 'contains': ['12.e1', '12.j1', '12.t1', '18.i1', '18.j1', '18.o1', '18.p1', '24.c1'], 'core': '12.e1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 18144, 12384, 10368, 15552, 36, 5712, 15984, 15624, 76], 'label': '31104.fx.6.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.d1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.d1', 'subgroup_fusion': None, 'weyl_group': '10368.fj'}
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id: 186246114
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1', '18.t1'], 'contains': ['72.r1', '72.s1', '72.u1', '72.v1', '72.ce1', '72.cf1', '72.cj1', '108.dj1', '108.dk1', '108.dl1', '108.dm1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1, 2592, 12096, 468, 15552, 10368, 22752, 16056], 'label': '31104.fx.36.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '36.bj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bj1', 'subgroup_fusion': None, 'weyl_group': '432.768'}
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id: 186246115
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.iy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ed1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dn1', '216.bf1', '216.hz1', '216.il1', '216.in1', '216.jd1', '216.ky1', '216.lf1'], 'contains': ['864.en1', '864.eq1', '864.fw1', '1296.gm1', '1296.hk1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [29077, 10368, 12138, 22752, 18576], 'label': '31104.fx.432.iy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.iy1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.iy1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 186246116
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.iz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.db1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dl1', '216.bg1', '216.hw1', '216.io1', '216.iq1', '216.iy1', '216.kz1', '216.lg1'], 'contains': ['864.el1', '864.er1', '864.et1', '864.hn1', '1296.gn1', '1296.hj1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [26485, 10368, 12138, 18576, 12096], 'label': '31104.fx.432.iz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '432.iz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.iz1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186247418
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.u1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.ep1', '576.z1', '576.bg1', '864.gm1', '864.hk1', '864.ia1'], 'contains': ['3456.r1', '5184.ba1', '5184.be1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [26047, 8304, 23836], 'label': '31104.fx.1728.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fx1', 'old_label': '1728.bv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.bv1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186246117
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ja1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.db1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dn1', '216.bh1', '216.hx1', '216.ip1', '216.ir1', '216.iz1', '216.kz1', '216.lg1'], 'contains': ['864.el1', '864.er1', '864.fq1', '1296.gr1', '1296.hk1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [29077, 10368, 12138, 18576, 12096], 'label': '31104.fx.432.ja1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '432.ja1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ja1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186246118
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.jb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.dg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.do1', '216.bb1', '216.hs1', '216.is1', '216.jc1', '216.je1', '216.la1', '216.lf1'], 'contains': ['864.en1', '864.es1', '864.fx1', '1296.gs1', '1296.hl1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26485, 10368, 14802, 22752, 18576], 'label': '31104.fx.432.jb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.jb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jb1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246119
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.jc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ec1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.do1', '216.bg1', '216.ht1', '216.it1', '216.iw1', '216.ja1', '216.lb1', '216.lg1'], 'contains': ['864.el1', '864.et1', '864.ft1', '1296.gt1', '1296.hl1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [26485, 10368, 14802, 18576, 12096], 'label': '31104.fx.432.jc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '432.jc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jc1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186246120
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.jd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dp1', '216.l1', '216.io1', '216.ip1', '216.ja1', '216.jb1', '216.kv1', '216.lj2'], 'contains': ['864.el1', '864.fa1', '864.fr1', '1296.gv1', '1296.hm1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [28567, 22752, 108, 18576, 12096], 'label': '31104.fx.432.jd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.jd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jd1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186246121
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.je1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dp1', '216.m1', '216.kw1', '216.lj1'], 'contains': ['864.em1', '864.fb1', '864.fs1', '1296.gw1', '1296.hm1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [18150, 10368, 18180, 16056, 12096], 'label': '31104.fx.432.je1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.k1', 'old_label': '432.je1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.je1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 186246122
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.jf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cr1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dp1', '216.n1', '216.ik1', '216.il1', '216.je1', '216.jf1', '216.kx1', '216.lk1'], 'contains': ['864.en1', '864.fc1', '864.fx1', '1296.gu1', '1296.hm1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [3943, 10368, 18684, 18576, 22752], 'label': '31104.fx.432.jf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.jf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jf1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 186246123
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.jg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cn1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dq1', '216.bc1', '216.it1', '216.iu1', '216.iy1', '216.iz1', '216.jz1', '216.lj2'], 'contains': ['864.el1', '864.ff2', '864.fr1', '1296.gy1', '1296.hn1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [28567, 22752, 2700, 18576, 12096], 'label': '31104.fx.432.jg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.jg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jg1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186246124
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.jh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dq1', '216.bd1', '216.ka1', '216.lj1'], 'contains': ['864.em1', '864.fg1', '864.fs1', '1296.gz1', '1296.hn1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [18150, 10368, 468, 16056, 12096], 'label': '31104.fx.432.jh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.k1', 'old_label': '432.jh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jh1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186246125
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.j1', '18.g1', '18.h1', '18.i1'], 'contains': ['72.cu1', '108.dn1', '108.do1', '108.dp1', '108.dq1', '144.bh1'], 'core': '216.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [36, 18576, 18144, 22828, 16056, 10368, 15552, 16080], 'label': '31104.fx.36.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.bk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bk1', 'subgroup_fusion': None, 'weyl_group': '3456.di'}
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id: 186246126
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ji1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dq1', '216.be1', '216.is1', '216.iv1', '216.jc1', '216.jd1', '216.kb1', '216.lk1'], 'contains': ['864.en1', '864.fh1', '864.fx1', '1296.gx1', '1296.hn1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [3943, 10368, 16092, 18576, 22752], 'label': '31104.fx.432.ji1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.ji1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ji1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186246127
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.jj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ej1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dr1', '216.bi1', '216.ht1', '216.io1', '216.ir1', '216.iu1', '216.lc1', '216.ll1'], 'contains': ['864.el1', '864.fk1', '864.fn1', '1296.ha1', '1296.ho1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 10368, 14802, 12096, 18576], 'label': '31104.fx.432.jj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.jj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jj1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 186246128
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.jk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.di1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dr1', '216.bk1', '216.hs1', '216.ik1', '216.in1', '216.iv1', '216.ld1', '216.lo1'], 'contains': ['864.en1', '864.fm1', '864.fv1', '1296.hb1', '1296.ho1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [5713, 10368, 14730, 18576, 22752], 'label': '31104.fx.432.jk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '432.jk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jk1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186246129
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.jl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ej1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ds1', '216.bj1', '216.hu1', '216.ip1', '216.iq1', '216.it1', '216.lc1', '216.ll1'], 'contains': ['864.el1', '864.fn1', '864.fu1', '1296.he1', '1296.hp1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [8305, 10368, 14802, 12096, 18576], 'label': '31104.fx.432.jl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.jl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jl1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246130
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.jm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ec1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dt1', '216.bh1', '216.hu1', '216.iu1', '216.ix1', '216.jb1', '216.lb1', '216.lg1'], 'contains': ['864.el1', '864.fq1', '864.ft1', '1296.hf1', '1296.hq1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [29077, 10368, 14802, 18576, 12096], 'label': '31104.fx.432.jm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '432.jm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jm1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186246131
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.jn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.el1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ds1', '216.bl1', '216.hv1', '216.il1', '216.im1', '216.is1', '216.ld1', '216.lo1'], 'contains': ['864.en1', '864.fv1', '864.fy1', '1296.hc1', '1296.hp1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [8305, 10368, 14730, 18576, 22752], 'label': '31104.fx.432.jn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '432.jn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jn1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186246132
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.jo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ed1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dt1', '216.bf1', '216.hv1', '216.iv1', '216.jd1', '216.jf1', '216.la1', '216.lf1'], 'contains': ['864.en1', '864.fw1', '864.fx1', '1296.hd1', '1296.hq1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [29077, 10368, 14802, 22752, 18576], 'label': '31104.fx.432.jo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.jo1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jo1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 186246133
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.jp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cz1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.du1', '216.bi1', '216.hw1', '216.ix1', '216.iz1', '216.ja1', '216.le1', '216.ll1'], 'contains': ['864.ek1', '864.el1', '864.fk1', '864.hq1', '1296.hg1', '1296.hr1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 10368, 12138, 18576, 12096], 'label': '31104.fx.432.jp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.jp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jp1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246134
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.jq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cz1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dv1', '216.bj1', '216.hx1', '216.iw1', '216.iy1', '216.jb1', '216.le1', '216.ll1'], 'contains': ['864.ek1', '864.el1', '864.fu1', '1296.hh1', '1296.hs1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [8305, 10368, 12138, 12096, 18576], 'label': '31104.fx.432.jq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.jq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jq1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 186246135
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.jr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.di1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.du1', '216.bk1', '216.hy1', '216.jd1', '216.je1', '216.lo1'], 'contains': ['864.en1', '864.fm1', '864.hs1', '1296.hr1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [5713, 10368, 12138, 18576, 22752], 'label': '31104.fx.432.jr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '432.jr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jr1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186246136
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1', '18.j1'], 'contains': ['72.de1', '108.dn1', '108.dr1', '108.ds1', '108.dt1', '144.bi1', '144.bj1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [36, 18576, 18144, 76, 16056, 12384, 15552, 16080], 'label': '31104.fx.36.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1', 'old_label': '36.bl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bl1', 'subgroup_fusion': None, 'weyl_group': '1728.47859'}
-
id: 186246137
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.js1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.el1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dv1', '216.bl1', '216.hz1', '216.jc1', '216.jf1', '216.lo1'], 'contains': ['864.en1', '864.fy1', '1296.hs1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [8305, 10368, 12138, 18576, 22752], 'label': '31104.fx.432.js1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '432.js1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.js1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186246138
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.jt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.dg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dw1', '216.bb1', '216.hs1', '216.im1', '216.jg1', '216.jk1', '216.ky1', '216.lq1'], 'contains': ['864.eq1', '864.es1', '864.fv1', '1296.ht1', '1296.hz1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26485, 10368, 14730, 22752, 18576], 'label': '31104.fx.432.jt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.jt1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jt1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 186246139
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ju1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.eb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dw1', '216.y1', '216.ht1', '216.iq1', '216.jh1', '216.jo1', '216.km1', '216.lr1'], 'contains': ['864.eo1', '864.et1', '864.fn1', '1296.ht1', '1296.ia1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26485, 12096, 14730, 22752, 18576], 'label': '31104.fx.432.ju1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.ju1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ju1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 186246140
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.jv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dx1', '216.l1', '216.ie1', '216.if1', '216.jo1', '216.jp1', '216.kv1', '216.lu1'], 'contains': ['864.eo1', '864.fa1', '864.fo1', '1296.hu1', '1296.ic1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26047, 22752, 108, 18576, 12096], 'label': '31104.fx.432.jv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.jv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jv1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186246141
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.jw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dx1', '216.m1', '216.kw1', '216.lv1'], 'contains': ['864.ep1', '864.fb1', '864.fp1', '1296.hu1', '1296.id1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [6, 10368, 18180, 16056, 12096], 'label': '31104.fx.432.jw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.k1', 'old_label': '432.jw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jw1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 186246142
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.jx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cr1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dx1', '216.n1', '216.ik1', '216.il1', '216.jk1', '216.jl1', '216.kx1', '216.lw1'], 'contains': ['864.eq1', '864.fc1', '864.fv1', '1296.hu1', '1296.ib1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [19135, 10368, 18684, 18576, 22752], 'label': '31104.fx.432.jx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.jx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jx1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 186246143
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.jy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cn1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dy1', '216.bc1', '216.ig1', '216.ih1', '216.jh1', '216.ji1', '216.jz1', '216.lu1'], 'contains': ['864.eo1', '864.ff2', '864.fo1', '1296.hv1', '1296.if1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26047, 22752, 2700, 18576, 12096], 'label': '31104.fx.432.jy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.jy1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jy1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 186246144
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.jz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dy1', '216.bd1', '216.ka1', '216.lv1'], 'contains': ['864.ep1', '864.fg1', '864.fp1', '1296.hv1', '1296.ig1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [6, 10368, 468, 16056, 12096], 'label': '31104.fx.432.jz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.k1', 'old_label': '432.jz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jz1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 186246145
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ka1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dy1', '216.be1', '216.im1', '216.in1', '216.jg1', '216.jj1', '216.kb1', '216.lw1'], 'contains': ['864.eq1', '864.fh1', '864.fv1', '1296.hv1', '1296.ie1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [19135, 10368, 16092, 18576, 22752], 'label': '31104.fx.432.ka1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.ka1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ka1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186246146
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.kb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dz1', '216.bo1', '216.ht1', '216.ie1', '216.ix1', '216.ji1', '216.ls1', '216.md1'], 'contains': ['864.eo1', '864.fk1', '864.ft1', '1296.hw1', '1296.ih1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 10368, 2670, 18576, 12096], 'label': '31104.fx.432.kb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.kb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.kb1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186246147
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.a1', '18.k1', '18.m1', '18.q1'], 'contains': ['72.cr1', '108.dq1', '108.du1', '144.bk1', '144.ep1', '144.eq1'], 'core': '216.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [36, 2592, 15552, 20812, 18576, 22752, 12096, 2664], 'label': '31104.fx.36.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.bm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bm1', 'subgroup_fusion': None, 'weyl_group': '3456.gu'}
-
id: 186246148
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.kc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dz1', '216.bm1', '216.hs1', '216.ik1', '216.jd1', '216.jj1', '216.lt1', '216.mb1'], 'contains': ['864.eq1', '864.fm1', '864.fx1', '1296.hw1', '1296.ii1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 10368, 2598, 18576, 22752], 'label': '31104.fx.432.kc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.kc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.kc1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186246149
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.kd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.eb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ea1', '216.z1', '216.hu1', '216.ir1', '216.ji1', '216.jp1', '216.km1', '216.lr1'], 'contains': ['864.eo1', '864.fn1', '864.fq1', '1296.hx1', '1296.il1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [29077, 12096, 14730, 22752, 18576], 'label': '31104.fx.432.kd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.kd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.kd1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246150
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ke1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.eb1', '216.bp1', '216.hu1', '216.if1', '216.iw1', '216.jh1', '216.ls1', '216.md1'], 'contains': ['864.eo1', '864.ft1', '864.fu1', '1296.hy1', '1296.im1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [8305, 10368, 2670, 18576, 12096], 'label': '31104.fx.432.ke1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.ke1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ke1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186246151
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.kf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ed1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ea1', '216.bf1', '216.hv1', '216.in1', '216.jj1', '216.jl1', '216.ky1', '216.lq1'], 'contains': ['864.eq1', '864.fv1', '864.fw1', '1296.hx1', '1296.ij1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [29077, 10368, 14730, 22752, 18576], 'label': '31104.fx.432.kf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.kf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.kf1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 186246152
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.kg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.u1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.eb1', '216.bn1', '216.hv1', '216.il1', '216.jc1', '216.jg1', '216.lt1', '216.mb1'], 'contains': ['864.eq1', '864.fx1', '864.fy1', '1296.hy1', '1296.ik1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [8305, 10368, 2598, 18576, 22752], 'label': '31104.fx.432.kg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.kg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.kg1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186246153
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.kh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ec1', '216.bm1', '216.hy1', '216.in1', '216.jk1', '216.mb1'], 'contains': ['864.eq1', '864.fm1', '864.hz1', '1296.in1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [5713, 10368, 6, 18576, 22752], 'label': '31104.fx.432.kh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.kh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.kh1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186246154
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ki1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ed1', '216.bn1', '216.hz1', '216.im1', '216.jl1', '216.mb1'], 'contains': ['864.eq1', '864.fy1', '1296.io1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [8305, 10368, 6, 18576, 22752], 'label': '31104.fx.432.ki1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.ki1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ki1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186246155
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.kj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.db1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dw1', '216.bg1', '216.hq1', '216.ig1', '216.jm1', '216.jo1', '216.kz1', '216.lx1'], 'contains': ['864.er1', '864.et1', '864.fo1', '1296.hz1', '1296.ia1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [26485, 10368, 14730, 18576, 12096], 'label': '31104.fx.432.kj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '432.kj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.kj1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186246156
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.kk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dx1', '216.k1', '216.io1', '216.ip1', '216.jo1', '216.jp1', '216.kn1', '216.me1'], 'contains': ['864.er1', '864.fa1', '864.fn1', '1296.ib1', '1296.ic1', '1296.id1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26047, 10368, 18684, 18576, 12096], 'label': '31104.fx.432.kk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.kk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.kk1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186246157
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.kl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dy1', '216.ba1', '216.iq1', '216.ir1', '216.jm1', '216.jn1', '216.jx1', '216.me1'], 'contains': ['864.er1', '864.ff1', '864.fn1', '1296.ie1', '1296.if1', '1296.ig1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26047, 10368, 16092, 18576, 12096], 'label': '31104.fx.432.kl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.kl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.kl1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186246158
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1', '12.k1', '18.o1'], 'contains': ['72.bt1', '72.cb1', '72.cx1', '108.do1', '108.dr1', '108.ds1', '108.dv1', '144.bl1'], 'core': '216.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [36, 72, 18144, 18576, 10924, 10368, 2016, 15552], 'label': '31104.fx.36.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '36.bn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bn1', 'subgroup_fusion': None, 'weyl_group': '1296.3551'}
-
id: 186246159
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.km1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dz1', '216.bo1', '216.hq1', '216.io1', '216.iz1', '216.jn1', '216.ly1', '216.mf1'], 'contains': ['864.er1', '864.fk1', '864.fr1', '1296.ih1', '1296.ii1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 10368, 2598, 18576, 12096], 'label': '31104.fx.432.km1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.km1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.km1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186246160
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.kn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.db1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ea1', '216.bh1', '216.hr1', '216.ih1', '216.jn1', '216.jp1', '216.kz1', '216.lx1'], 'contains': ['864.er1', '864.fo1', '864.fq1', '1296.ij1', '1296.il1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [29077, 10368, 14730, 18576, 12096], 'label': '31104.fx.432.kn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '432.kn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.kn1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186246161
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ko1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.eb1', '216.bp1', '216.hr1', '216.ip1', '216.iy1', '216.jm1', '216.ly1', '216.mf1'], 'contains': ['864.er1', '864.fr1', '864.fu1', '1296.ik1', '1296.im1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [8305, 10368, 2598, 18576, 12096], 'label': '31104.fx.432.ko1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.ko1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ko1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186246162
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.kp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ec1', '216.bo1', '216.hw1', '216.ih1', '216.ir1', '216.jo1', '216.md1', '216.mf1'], 'contains': ['864.eo1', '864.er1', '864.fk1', '864.if1', '1296.in1', '1296.ip1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 10368, 6, 18576, 12096], 'label': '31104.fx.432.kp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.kp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.kp1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186246163
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.kq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ed1', '216.bp1', '216.hx1', '216.ig1', '216.iq1', '216.jp1', '216.md1', '216.mf1'], 'contains': ['864.eo1', '864.er1', '864.fu1', '1296.io1', '1296.iq1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [8305, 10368, 6, 18576, 12096], 'label': '31104.fx.432.kq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.kq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.kq1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186246164
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.kr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ee1', '216.o1', '216.ik1', '216.je1', '216.jk1', '216.mg1'], 'contains': ['864.es1', '864.fc1', '864.fm1', '864.ig1', '1296.ir1', '1296.is1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1, 10368, 15588, 2592, 22752], 'label': '31104.fx.432.kr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.kr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.kr1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186246165
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ks1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ef1', '216.br1', '216.im1', '216.is1', '216.jc1', '216.jg1', '216.ke1', '216.mg1'], 'contains': ['864.es1', '864.fh1', '864.fy1', '1296.it1', '1296.it2', '1296.iu1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [15985, 10368, 468, 2592, 22752], 'label': '31104.fx.432.ks1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.ks1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ks1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186246166
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.kt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.dg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.eg1', '216.bb1', '216.ia1', '216.ik1', '216.is1', '216.jg1', '216.la1', '216.lq1'], 'contains': ['864.es1', '864.fv1', '864.fx1', '1296.iv1', '1296.iw1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26485, 10368, 12210, 22752, 18576], 'label': '31104.fx.432.kt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.kt1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.kt1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246167
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ku1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ee1', '216.p1', '216.ie1', '216.io1', '216.ja1', '216.jo1', '216.mh1', '216.mi1'], 'contains': ['864.et1', '864.fa1', '864.fk1', '864.il1', '1296.ir1', '1296.ix1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [20737, 22752, 15588, 2592, 1728], 'label': '31104.fx.432.ku1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.ku1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ku1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186246168
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.kv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ee1', '216.q1', '216.mj1'], 'contains': ['864.eu1', '864.fd1', '864.fl1', '864.im1', '864.im2', '1296.is1', '1296.ix1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [20737, 12384, 15588, 2592, 1728], 'label': '31104.fx.432.kv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.p1', 'old_label': '432.kv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.kv1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186246169
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.a1', '12.j1', '18.l1', '18.n1', '18.p1'], 'contains': ['72.b1', '108.dp1', '108.dq1', '108.dt1', '108.dv1', '144.bn1', '144.er1'], 'core': '72.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [36, 2592, 15552, 76, 18576, 10368, 12384, 2664], 'label': '31104.fx.36.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '36.bo1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bo1', 'subgroup_fusion': None, 'weyl_group': '10368.fj'}
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id: 186246170
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.kw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ef1', '216.bu1', '216.ig1', '216.it1', '216.iy1', '216.jh1', '216.kg1', '216.mh1'], 'contains': ['864.et1', '864.ff2', '864.fu1', '1296.it1', '1296.iy1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5617, 22752, 468, 2592, 1728], 'label': '31104.fx.432.kw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.kw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.kw1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186246171
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.kw2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ef1', '216.bu1', '216.ii1', '216.iq1', '216.iw1', '216.jm1', '216.kf1', '216.mi1'], 'contains': ['864.et1', '864.ff1', '864.fu1', '1296.it2', '1296.iy1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5617, 22752, 16020, 2592, 1728], 'label': '31104.fx.432.kw2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.kw2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.kw2', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186246172
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.kx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ef1', '216.bv1', '216.kh1', '216.mj1'], 'contains': ['864.eu1', '864.fi1', '864.ga1', '1296.iu1', '1296.iy1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [8209, 12384, 3060, 2592, 1728], 'label': '31104.fx.432.kx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.p1', 'old_label': '432.kx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.kx1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 186246173
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ky1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.eb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.eg1', '216.y1', '216.ib1', '216.io1', '216.it1', '216.jm1', '216.ko1', '216.lr1'], 'contains': ['864.et1', '864.fn1', '864.fr1', '1296.iv1', '1296.iz1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26485, 12096, 12210, 22752, 18576], 'label': '31104.fx.432.ky1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.ky1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ky1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246174
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.kz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ec1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.eg1', '216.bg1', '216.ib1', '216.ie1', '216.ii1', '216.jh1', '216.lb1', '216.lx1'], 'contains': ['864.et1', '864.fo1', '864.ft1', '1296.iw1', '1296.iz1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [26485, 10368, 12210, 18576, 12096], 'label': '31104.fx.432.kz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '432.kz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.kz1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186246175
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.la1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.eh1', '216.r1', '216.if1', '216.ip1', '216.jb1', '216.jp1', '216.mh1', '216.mi1'], 'contains': ['864.fa1', '864.fq1', '864.fu1', '1296.ja1', '1296.jc1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5617, 22752, 15588, 2592, 1728], 'label': '31104.fx.432.la1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.la1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.la1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186246176
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.lb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.eh1', '216.t1', '216.il1', '216.jf1', '216.jl1', '216.mg1'], 'contains': ['864.fc1', '864.fw1', '864.fy1', '1296.ja1', '1296.jb1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [15985, 10368, 15588, 2592, 22752], 'label': '31104.fx.432.lb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.lb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.lb1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 186246177
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.lc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.eh1', '216.v1', '216.mj1'], 'contains': ['864.fd1', '864.fz1', '864.ga1', '1296.jb1', '1296.jc1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [8209, 12384, 15588, 2592, 1728], 'label': '31104.fx.432.lc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.p1', 'old_label': '432.lc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.lc1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186246178
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ld1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ei1', '216.ch1', '216.ih1', '216.iu1', '216.iz1', '216.ji1', '216.kg1', '216.mh1'], 'contains': ['864.ff2', '864.fk1', '864.fq1', '1296.jd1', '1296.je1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [20737, 22752, 468, 2592, 1728], 'label': '31104.fx.432.ld1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.ld1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ld1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186246179
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ld2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ei1', '216.ch1', '216.ij1', '216.ir1', '216.ix1', '216.jn1', '216.kf1', '216.mi1'], 'contains': ['864.ff1', '864.fk1', '864.fq1', '1296.jd1', '1296.je2'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [20737, 22752, 16020, 2592, 1728], 'label': '31104.fx.432.ld2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.ld2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ld2', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186246180
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1', '18.r1'], 'contains': ['72.bu1', '72.bv1', '72.cc1', '72.cd1', '72.da1', '108.ds1', '108.dw1', '144.bo1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [36, 72, 18144, 18576, 556, 12384, 12096, 15552], 'label': '31104.fx.36.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.r1', 'old_label': '36.bp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bp1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
-
id: 186246181
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.le1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ei1', '216.ci1', '216.kh1', '216.mj1'], 'contains': ['864.fi1', '864.fl1', '864.fz1', '1296.jd1', '1296.jf1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [20737, 12384, 3060, 2592, 1728], 'label': '31104.fx.432.le1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.p1', 'old_label': '432.le1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.le1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 186246182
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.lf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ei1', '216.cj1', '216.in1', '216.iv1', '216.jd1', '216.jj1', '216.ke1', '216.mg1'], 'contains': ['864.fh1', '864.fm1', '864.fw1', '1296.je1', '1296.je2', '1296.jf1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1, 10368, 468, 2592, 22752], 'label': '31104.fx.432.lf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.lf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.lf1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186246183
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.lg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cu1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ej1', '216.ba1', '216.it1', '216.iu1', '216.jh1', '216.ji1', '216.ki1', '216.kn1'], 'contains': ['864.ff2', '864.fn1', '864.ft1', '1296.jg1', '1296.ji1', '1296.jj1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [10855, 10368, 2628, 18576, 12096], 'label': '31104.fx.432.lg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.lg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.lg1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 186246184
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.lh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ej1', '216.bc1', '216.ii1', '216.ij1', '216.jm1', '216.jn1', '216.kj1', '216.kv1'], 'contains': ['864.ff1', '864.fo1', '864.fr1', '1296.jh1', '1296.ji1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [28567, 22752, 2628, 18576, 12096], 'label': '31104.fx.432.lh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.lh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.lh1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186246185
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.li1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ej1', '216.bd1', '216.kk1', '216.kw1'], 'contains': ['864.fg2', '864.fp1', '864.fs1', '1296.jh1', '1296.jj1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [18150, 10368, 18612, 16056, 12096], 'label': '31104.fx.432.li1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.k1', 'old_label': '432.li1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.li1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186246186
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.lj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ej1', '216.be1', '216.is1', '216.iv1', '216.jg1', '216.jj1', '216.kl1', '216.kx1'], 'contains': ['864.fh1', '864.fv1', '864.fx1', '1296.jg1', '1296.jh1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [3943, 10368, 2628, 18576, 22752], 'label': '31104.fx.432.lj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.lj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.lj1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186246187
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.lk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ej1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ek1', '216.bi1', '216.ib1', '216.ji1', '216.jn1', '216.jo1', '216.kp1', '216.lc1'], 'contains': ['864.fk1', '864.fn1', '864.fo1', '1296.jk1', '1296.jm1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 10368, 12210, 12096, 18576], 'label': '31104.fx.432.lk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.lk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.lk1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246188
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ll1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.el1', '216.bo1', '216.ib1', '216.ij1', '216.iu1', '216.ja1', '216.ls1', '216.ly1'], 'contains': ['864.fk1', '864.fr1', '864.ft1', '1296.jl1', '1296.jn1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 10368, 78, 18576, 12096], 'label': '31104.fx.432.ll1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.ll1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ll1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186246189
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.lm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.di1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ek1', '216.bk1', '216.ia1', '216.jj1', '216.jk1', '216.ld1'], 'contains': ['864.fm1', '864.fv1', '1296.jm1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [5713, 10368, 12210, 18576, 22752], 'label': '31104.fx.432.lm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '432.lm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.lm1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186246190
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ln1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.el1', '216.bm1', '216.ia1', '216.iv1', '216.je1', '216.lt1'], 'contains': ['864.fm1', '864.fx1', '1296.jn1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [5713, 10368, 78, 18576, 22752], 'label': '31104.fx.432.ln1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.ln1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ln1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186246191
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.l1', '18.k1', '18.u1', '18.be1'], 'contains': ['72.cr1', '108.dx1', '108.dy1', '108.dz1', '144.et1'], 'core': '216.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [12138, 2664, 18576, 20812, 22752, 15552, 2592, 12096], 'label': '31104.fx.36.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.bq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bq1', 'subgroup_fusion': None, 'weyl_group': '1152.155790'}
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id: 186246192
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.lo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.eb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.em1', '216.z1', '216.ic1', '216.ip1', '216.iu1', '216.jn1', '216.ko1', '216.lr1'], 'contains': ['864.fn1', '864.fq1', '864.fr1', '1296.jo1', '1296.js1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [29077, 12096, 78, 10368, 18576], 'label': '31104.fx.432.lo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.lo1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.lo1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 186246233
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.my1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.ek1', '144.fb1', '144.fj1', '216.jq1', '216.lm1', '216.lz1'], 'contains': ['864.gf1', '1296.km1', '1296.ku1', '1728.bq1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [6, 22752, 20812, 2664, 18576], 'label': '31104.fx.432.my1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.dj1', 'old_label': '432.my1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.my1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
-
id: 186246193
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.lp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ec1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.em1', '216.bh1', '216.ic1', '216.if1', '216.ij1', '216.ji1', '216.lb1', '216.lx1'], 'contains': ['864.fo1', '864.fq1', '864.ft1', '1296.jp1', '1296.js1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [29077, 22752, 78, 18576, 12096], 'label': '31104.fx.432.lp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '432.lp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.lp1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186246194
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.lq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ej1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.en1', '216.bj1', '216.ic1', '216.jh1', '216.jm1', '216.jp1', '216.kp1', '216.lc1'], 'contains': ['864.fn1', '864.fo1', '864.fu1', '1296.jq1', '1296.jt1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [8305, 10368, 12210, 12096, 18576], 'label': '31104.fx.432.lq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.lq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.lq1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246195
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.lr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.eo1', '216.bp1', '216.ic1', '216.ii1', '216.it1', '216.jb1', '216.ls1', '216.ly1'], 'contains': ['864.fr1', '864.ft1', '864.fu1', '1296.jr1', '1296.ju1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [8305, 10368, 78, 18576, 12096], 'label': '31104.fx.432.lr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.lr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.lr1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186246196
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ls1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ed1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.em1', '216.bf1', '216.id1', '216.il1', '216.iv1', '216.jj1', '216.la1', '216.lq1'], 'contains': ['864.fv1', '864.fw1', '864.fx1', '1296.jo1', '1296.jp1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [29077, 10368, 12210, 22752, 18576], 'label': '31104.fx.432.ls1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.ls1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ls1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 186246197
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.lt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.el1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.en1', '216.bl1', '216.id1', '216.jg1', '216.jl1', '216.ld1'], 'contains': ['864.fv1', '864.fy1', '1296.jq1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [8305, 10368, 12210, 18576, 22752], 'label': '31104.fx.432.lt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '432.lt1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.lt1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186246198
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.lu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.eo1', '216.bn1', '216.id1', '216.is1', '216.jf1', '216.lt1'], 'contains': ['864.fx1', '864.fy1', '1296.jr1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [8305, 10368, 78, 18576, 22752], 'label': '31104.fx.432.lu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.lu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.lu1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186246199
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.lv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.dp1', '144.er1', '216.jr1', '216.js1', '216.ju1'], 'contains': ['864.ge1', '1296.jv1', '1296.jw1', '1728.u1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [36, 10368, 22828, 2664, 18576], 'label': '31104.fx.432.lv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.gd1', 'old_label': '432.lv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.lv1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
-
id: 186246200
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.lw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.dq1', '144.ep1', '144.eq1', '144.er1', '216.jq1', '216.jt1', '216.jv1'], 'contains': ['864.gf1', '1296.jv1', '1296.jw2', '1728.v1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [36, 22752, 20812, 2664, 18576], 'label': '31104.fx.432.lw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ge1', 'old_label': '432.lw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.lw1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
-
id: 186246201
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.lx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.dt1', '144.er1', '216.jw1'], 'contains': ['864.gk1', '1296.jv1', '1296.jx1', '1728.y1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [36, 12384, 16080, 15624, 432], 'label': '31104.fx.432.lx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.jw1', 'old_label': '432.lx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.lx1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186246202
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.c1', '18.g1', '18.v1', '18.bf1'], 'contains': ['72.cu1', '108.dy1', '108.eb1', '108.ef1', '108.eg1', '576.q1'], 'core': '216.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [12138, 15624, 15984, 20812, 5712, 15552, 2592, 22752], 'label': '31104.fx.36.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.br1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.br1', 'subgroup_fusion': None, 'weyl_group': '1152.157852'}
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id: 186246203
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ly1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.es1', '216.co1', '216.cp1', '216.jx1', '216.kc1', '216.kf1', '216.kj1', '216.kk1'], 'contains': ['864.ef1', '864.eg1', '864.ff1', '864.fg2', '864.gb1', '1296.jw1', '1296.jy1', '1296.jz1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [36, 10368, 16056, 18576, 12096], 'label': '31104.fx.432.ly1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '432.ly1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ly1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186246204
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.lz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ep1', '144.es1', '216.cp1', '216.jy1', '216.jz1', '216.kg1', '216.ki1'], 'contains': ['864.ef1', '864.ff2', '864.gc1', '1296.jw2', '1296.jy1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [36, 10368, 18576, 2592, 12096], 'label': '31104.fx.432.lz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '432.lz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.lz1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
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id: 186246205
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ma1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.eq1', '144.es1', '216.co1', '216.ka1'], 'contains': ['864.eg1', '864.fg1', '864.gd1', '1296.jw2', '1296.jz1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [36, 10368, 16056, 432, 12096], 'label': '31104.fx.432.ma1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '432.ma1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ma1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
-
id: 186246206
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.mb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.er1', '144.es1', '216.cq1', '216.kb1', '216.kd1', '216.ke1', '216.kl1'], 'contains': ['864.eh1', '864.fh1', '864.gi1', '1296.jw1', '1296.jw2', '1296.jx1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [36, 10368, 16056, 432, 22752], 'label': '31104.fx.432.mb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '432.mb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.mb1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
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id: 186246207
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.mc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.es1', '216.cr1', '216.cs1', '216.kh1'], 'contains': ['864.ei1', '864.ej1', '864.fi1', '864.fj1', '864.gj1', '1296.jx1', '1296.jy1', '1296.jz1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [36, 12384, 16056, 432, 12096], 'label': '31104.fx.432.mc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '432.mc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.mc1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246208
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.md1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.gc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.eu1', '216.ct1', '216.jx1', '216.km1', '216.kn1', '216.ko1', '216.kp1', '216.ll1'], 'contains': ['864.ek1', '864.fn1', '864.gb1', '1296.ka1', '1296.kb1', '1296.kc1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [17371, 18576, 16056, 12096, 10368], 'label': '31104.fx.432.md1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.md1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.md1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
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id: 186246209
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.me1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.me1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.et1', '144.ev1', '216.ct1', '216.jy1', '216.kq1', '216.kt1', '216.le1'], 'contains': ['864.ek1', '864.gc1', '1296.kd1', '1296.ke1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [17371, 10368, 18576, 2592, 12096], 'label': '31104.fx.432.me1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '432.me1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.me1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186246210
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.mf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.dy1', '144.et1', '144.ew1', '216.jq1', '216.kr1', '216.lp1'], 'contains': ['864.gf1', '1296.kd1', '1296.kf1', '1728.bd1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [12138, 18576, 20812, 22752, 2664], 'label': '31104.fx.432.mf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.di1', 'old_label': '432.mf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.mf1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186246211
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.mg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.dz1', '144.et1', '144.ex1', '216.ks1'], 'contains': ['864.gh1', '1296.kd1', '1296.kg1', '1728.be1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [12138, 18576, 13900, 22752, 2664], 'label': '31104.fx.432.mg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.el1', 'old_label': '432.mg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.mg1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
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id: 186246212
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.mh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.mh1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.eu1', '144.ey1', '216.cv1', '216.jz1', '216.kv1', '216.kz1', '216.lb1', '216.lc1', '216.le1'], 'contains': ['864.el1', '864.fo1', '864.gc1', '1296.kb1', '1296.kh1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [17371, 22752, 16056, 12096, 18576], 'label': '31104.fx.432.mh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '432.mh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.mh1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246213
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.gc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.b1', '12.l1', '18.s1', '18.w1', '18.z1'], 'contains': ['72.a1', '72.x1', '72.bc1', '108.dx1', '108.ea1', '108.ee1'], 'core': '72.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [17371, 10368, 18576, 16056, 12096, 22752, 2592, 15552], 'label': '31104.fx.36.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '36.bs1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bs1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
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id: 186246214
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.mi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.gc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.eu1', '144.ez1', '216.cu1', '216.ka1', '216.kw1'], 'contains': ['864.em1', '864.fp1', '864.gd1', '1296.kc1', '1296.kh1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [12138, 10368, 432, 12096, 16056], 'label': '31104.fx.432.mi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.g1', 'old_label': '432.mi1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.mi1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246215
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.mj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.z1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.eb1', '144.fa1', '216.jr1', '216.ku1', '216.ln1'], 'contains': ['864.ge1', '1296.ka1', '1296.ki1', '1728.bg1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [12138, 432, 22752, 21192, 16056], 'label': '31104.fx.432.mj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.gd1', 'old_label': '432.mj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.mj1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186246216
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.mk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.gc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.eu1', '144.fa1', '216.cw1', '216.kb1', '216.kx1', '216.ky1', '216.la1', '216.ld1', '216.lo1'], 'contains': ['864.en1', '864.fv1', '864.gi1', '1296.ka1', '1296.kh1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [12138, 10368, 432, 22752, 16056], 'label': '31104.fx.432.mk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '432.mk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.mk1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246217
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ml1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.gc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ev1', '216.cu1', '216.cv1', '216.kc1', '216.lg1', '216.lj1', '216.lj2', '216.ll1'], 'contains': ['864.el1', '864.em1', '864.gb1', '1296.ke1', '1296.kj1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [17371, 22752, 2592, 18576, 12096], 'label': '31104.fx.432.ml1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '432.ml1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ml1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186246218
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.mm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.bc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.ec1', '144.ew1', '216.js1', '216.lh1', '216.ln1'], 'contains': ['864.ge1', '1296.kf1', '1296.kj1', '1728.bh1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [17371, 22752, 5712, 15984, 2592], 'label': '31104.fx.432.mm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.dj1', 'old_label': '432.mm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.mm1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186246219
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.mn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.ed1', '144.ex1', '216.li1'], 'contains': ['864.gh3', '1296.kg1', '1296.kj1', '1728.bi1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [12138, 10368, 13900, 2664, 18576], 'label': '31104.fx.432.mn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.es1', 'old_label': '432.mn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.mn1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186246220
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.mo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.gc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ev1', '144.ew1', '144.ex1', '216.cw1', '216.kd1', '216.lf1', '216.lk1', '216.lo1'], 'contains': ['864.en1', '864.gi1', '1296.kd1', '1296.kj1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [17371, 22752, 18576, 2592, 10368], 'label': '31104.fx.432.mo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '432.mo1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.mo1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
-
id: 186246221
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.mp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.a1', '144.ey1', '144.ez1', '144.fa1', '216.jt1', '216.lm1', '216.lp1'], 'contains': ['864.gf1', '1296.kh1', '1296.ki1', '1728.bm1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [12138, 432, 21192, 10368, 16056], 'label': '31104.fx.432.mp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.x1', 'old_label': '432.mp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.mp1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
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id: 186246222
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.mq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.z1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.eh1', '144.fb1', '216.js1', '216.ku1', '216.mc1'], 'contains': ['864.ge1', '1296.kl1', '1296.km1', '1296.kn1', '1728.bn1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [6, 18576, 76, 10368, 2664], 'label': '31104.fx.432.mq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.gd1', 'old_label': '432.mq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.mq1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186246223
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.mr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.ka1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fc1', '144.fe1', '144.fg1', '216.cy1', '216.jz1', '216.kq1', '216.kv1', '216.lr1', '216.ls1', '216.mf1'], 'contains': ['864.eo1', '864.fr1', '864.gc1', '1296.kk1', '1296.kp1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [6, 12096, 2592, 10368, 18576], 'label': '31104.fx.432.mr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.mr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.mr1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246224
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '3.b1'], 'contains': ['12.a1', '12.l1', '12.n1', '18.k1', '18.l1', '18.s1', '24.q1'], 'core': '12.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [26047, 22752, 15984, 2592, 10368, 36, 15624, 12096, 15552, 5712], 'label': '31104.fx.6.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '6.e1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.e1', 'subgroup_fusion': None, 'weyl_group': '10368.je'}
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id: 186246225
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.c1', '12.l1', '18.l1', '18.x1', '18.bg1'], 'contains': ['72.b1', '108.dy1', '108.ec1', '108.ee1', '144.ew1'], 'core': '72.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [17371, 15984, 2592, 5712, 15624, 22752, 15552, 10368], 'label': '31104.fx.36.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '36.bt1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bt1', 'subgroup_fusion': None, 'weyl_group': '3456.de'}
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id: 186246226
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ms1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ep1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fd1', '144.ff1', '144.fg1', '216.cx1', '216.ka1', '216.kw1'], 'contains': ['864.ep1', '864.fs1', '864.gd1', '1296.kk1', '1296.kq1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [6, 12096, 432, 10368, 16056], 'label': '31104.fx.432.ms1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.k1', 'old_label': '432.ms1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ms1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246227
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.mt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.ej1', '144.fc1', '144.fd1', '144.fh1', '216.jt1', '216.kr1', '216.lz1'], 'contains': ['864.gf1', '1296.kk1', '1296.kr1', '1728.bp1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [6, 432, 10368, 21192, 16056], 'label': '31104.fx.432.mt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ge1', 'old_label': '432.mt1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.mt1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186246228
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.mu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.el1', '144.fe1', '144.ff1', '144.fh1', '216.ma1'], 'contains': ['864.gg1', '1296.kk1', '1296.ks1', '1728.br1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [26047, 18576, 22752, 18148, 16056], 'label': '31104.fx.432.mu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ma1', 'old_label': '432.mu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.mu1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186246229
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.mv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.en1', '144.fc1', '144.ff1', '144.fi1', '216.ks1'], 'contains': ['864.gh1', '1296.kk1', '1296.kt1', '1728.bt1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [6, 2592, 10368, 19536, 18576], 'label': '31104.fx.432.mv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ks1', 'old_label': '432.mv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.mv1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186246230
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.mv2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.en1', '144.fd1', '144.fe1', '144.ff1', '144.fi1'], 'contains': ['864.gh2', '1296.kk1', '1296.kt2', '1728.bt1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [26047, 18576, 22752, 4540, 16056], 'label': '31104.fx.432.mv2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.mv2', 'old_label': '432.mv2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.mv2', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186246231
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.mw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ep1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fg1', '144.fh1', '144.fi1', '216.cz1', '216.kb1', '216.kx1', '216.lf1', '216.lq1', '216.lt1', '216.mb1'], 'contains': ['864.eq1', '864.fx1', '864.gi1', '1296.kk1', '1296.ko1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [6, 22752, 432, 10368, 16056], 'label': '31104.fx.432.mw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.mw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.mw1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246232
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.mx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ep1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fl1', '216.cx1', '216.cy1', '216.kc1', '216.km1', '216.lu1', '216.lv1', '216.md1'], 'contains': ['864.eo1', '864.ep1', '864.gb1', '1296.kl1', '1296.kv1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [6, 12096, 16056, 18576, 10368], 'label': '31104.fx.432.mx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '432.mx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.mx1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186246234
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.mz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.em1', '144.fb1', '144.fk1', '216.ma1'], 'contains': ['864.gg1', '1296.kn1', '1296.ku1', '1728.bs1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [26047, 10368, 28464, 15984, 2592], 'label': '31104.fx.432.mz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.fb1', 'old_label': '432.mz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.mz1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186246235
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.na1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ep1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fb1', '144.fl1', '216.cz1', '216.kd1', '216.ky1', '216.lw1', '216.mb1'], 'contains': ['864.eq1', '864.gi1', '1296.kl1', '1296.ku1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [26047, 10368, 18576, 2592, 22752], 'label': '31104.fx.432.na1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '432.na1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.na1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
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id: 186246236
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.l1', '12.m1', '18.y1'], 'contains': ['72.cz1', '108.dz1', '108.ed1', '108.ee1', '144.ex1'], 'core': '216.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [12138, 18576, 2592, 24268, 2664, 10368, 15552, 22752], 'label': '31104.fx.36.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1', 'old_label': '36.bu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bu1', 'subgroup_fusion': None, 'weyl_group': '1728.32131'}
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id: 186246237
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.nb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ep1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fg1', '216.da1', '216.jx1', '216.kn1', '216.lg1', '216.lx1', '216.ly1', '216.md1'], 'contains': ['864.er1', '864.ft1', '864.gb1', '1296.ko1', '1296.kp1', '1296.kq1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [26047, 10368, 16056, 18576, 12096], 'label': '31104.fx.432.nb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '432.nb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.nb1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186246238
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.nc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.bc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.ev1', '144.fh1', '216.jr1', '216.lh1', '216.mc1'], 'contains': ['864.ge1', '1296.ko1', '1296.kr1', '1296.ks1', '1728.cb1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [6, 432, 21192, 22752, 16056], 'label': '31104.fx.432.nc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.dj1', 'old_label': '432.nc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.nc1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186246239
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.nd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.ew1', '144.fi1', '216.li1'], 'contains': ['864.gh3', '1296.ko1', '1296.kt1', '1296.kt2', '1728.cc1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [26047, 18576, 20452, 10368, 16056], 'label': '31104.fx.432.nd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.es1', 'old_label': '432.nd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.nd1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
-
id: 186246240
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ne1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.kj1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fj1', '144.fk1', '144.fl1', '216.da1', '216.jy1', '216.kz1', '216.me1', '216.mf1'], 'contains': ['864.er1', '864.gc1', '1296.ku1', '1296.kv1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [6, 22752, 16056, 18576, 12096], 'label': '31104.fx.432.ne1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '432.ne1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ne1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
-
id: 186246241
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.nf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fm1', '144.fn1', '144.fo1', '216.db1', '216.ke1', '216.ky1', '216.la1', '216.lf1', '216.lq1', '216.mg1'], 'contains': ['864.es1', '864.fw1', '864.gi1', '1296.kw1', '1296.kw2', '1296.kx1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [10405, 2592, 18576, 22752, 10368], 'label': '31104.fx.432.nf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.nf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.nf1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 186246242
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ng1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fm1', '216.dc1', '216.kf1', '216.km1', '216.ko1', '216.lg1', '216.lx1', '216.mh1'], 'contains': ['864.et1', '864.fq1', '864.gb1', '1296.kw1', '1296.ky1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [10405, 1728, 18576, 22752, 2592], 'label': '31104.fx.432.ng1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '432.ng1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ng1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246243
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.nh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.dd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fm1', '144.fp1', '216.dc1', '216.kg1', '216.kq1', '216.kz1', '216.lb1', '216.lr1', '216.mi1'], 'contains': ['864.et1', '864.fq1', '864.gc1', '1296.kw2', '1296.ky1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [10405, 1728, 18576, 10368, 2592], 'label': '31104.fx.432.nh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '432.nh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.nh1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246244
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ni1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.bu1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.fa1', '144.fn1', '216.ju1', '216.ku1', '216.lh1'], 'contains': ['864.ge1', '1296.kw1', '1296.kz1', '1728.cg1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [10405, 2592, 10368, 12460, 432], 'label': '31104.fx.432.ni1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.dj1', 'old_label': '432.ni1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ni1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186246245
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.nj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.bj1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.fb1', '144.fn1', '144.fp1', '216.jv1', '216.kr1', '216.lm1'], 'contains': ['864.gf1', '1296.kw2', '1296.kz1', '1728.ch1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [10405, 2592, 10368, 16080, 18576], 'label': '31104.fx.432.nj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.dj1', 'old_label': '432.nj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.nj1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186246246
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.nk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.bj1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.fd1', '144.fo1', '144.fp1', '216.ks1'], 'contains': ['864.gh1', '1296.kw2', '1296.la1', '1728.cj1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [10405, 2592, 22752, 24268, 432], 'label': '31104.fx.432.nk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.es1', 'old_label': '432.nk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.nk1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186246247
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.b1', '18.m1', '18.bb1', '18.be1'], 'contains': ['72.cr1', '108.a1', '108.ea1', '144.ey1', '144.ez1'], 'core': '108.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [12138, 16056, 432, 12096, 10368, 15552, 18144, 5712], 'label': '31104.fx.36.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '36.bv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bv1', 'subgroup_fusion': None, 'weyl_group': '3456.gu'}
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id: 186246248
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.nk2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.fd2', '144.fo1', '216.li1'], 'contains': ['864.gh3', '1296.kw1', '1296.la1', '1728.cj2'], 'core': '10368.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [10405, 2592, 10368, 24268, 432], 'label': '31104.fx.432.nk2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.es1', 'old_label': '432.nk2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.nk2', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186246249
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.nl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fm1', '216.dd1', '216.kh1', '216.mj1'], 'contains': ['864.eu1', '864.fz1', '864.gj1', '1296.kx1', '1296.ky1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [10405, 1728, 3024, 12384, 2592], 'label': '31104.fx.432.nl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.h1', 'old_label': '432.nl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.nl1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246250
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.nm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.fh1', '144.fn1', '216.jw1'], 'contains': ['864.gk1', '1296.kx1', '1296.kz1', '1728.cn1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [10405, 2592, 12384, 16080, 18576], 'label': '31104.fx.432.nm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.ef1', 'old_label': '432.nm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.nm1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186246251
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.nn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.fj1', '144.fo1'], 'contains': ['864.gl1', '1296.kx1', '1296.la1', '1728.cp1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [10405, 2592, 12384, 24268, 432], 'label': '31104.fx.432.nn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fo1', 'old_label': '432.nn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.nn1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186246252
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.no1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fq1', '216.co1', '216.de1', '216.df1', '216.lj1', '216.lv1', '216.ml1', '216.mm1'], 'contains': ['864.ev1', '864.ew2', '864.fb1', '864.fg1', '864.gb1', '1296.lb1', '1296.ld1', '1296.le1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [18180, 10368, 16056, 18576, 12096], 'label': '31104.fx.432.no1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bb1', 'old_label': '432.no1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.no1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246253
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.no2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fq1', '216.cp1', '216.de1', '216.kn1', '216.lj2', '216.lu1', '216.mh1', '216.mm2'], 'contains': ['864.ew1', '864.fa1', '864.ff2', '864.gb1', '1296.lb1', '1296.ld2', '1296.le2'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [2628, 10368, 16056, 18576, 12096], 'label': '31104.fx.432.no2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '432.no2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.no2', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186246254
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.np1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fq1', '216.cp1', '216.df1', '216.kt1', '216.kv1', '216.me1', '216.mi1', '216.mk1'], 'contains': ['864.ev1', '864.fa1', '864.ff1', '864.gc1', '1296.lb2', '1296.ld1', '1296.ld2'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [16092, 10368, 18576, 2592, 12096], 'label': '31104.fx.432.np1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '432.np1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.np1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186246255
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.nq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fq1', '216.co1', '216.de1', '216.kw1'], 'contains': ['864.ew1', '864.ew2', '864.fb1', '864.fg2', '864.gd1', '1296.lb2', '1296.le1', '1296.le2'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [18180, 10368, 16056, 432, 12096], 'label': '31104.fx.432.nq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bb1', 'old_label': '432.nq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.nq1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246256
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.nr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fq1', '216.cq1', '216.dg1', '216.kx1', '216.lk1', '216.lw1', '216.mg1', '216.mn1'], 'contains': ['864.ex1', '864.fc1', '864.fh1', '864.gi1', '1296.lb1', '1296.lb2', '1296.lc1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [18180, 10368, 16056, 432, 22752], 'label': '31104.fx.432.nr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '432.nr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.nr1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186246257
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ns1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fq1', '216.cr1', '216.di1', '216.mj1'], 'contains': ['864.ez2', '864.ez3', '864.fd1', '864.fi1', '864.gj1', '1296.lc1', '1296.ld2', '1296.le1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [18252, 12384, 16056, 432, 12096], 'label': '31104.fx.432.ns1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '432.ns1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ns1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246258
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.c1', '18.h1', '18.bc1', '18.bf1'], 'contains': ['72.cu1', '108.a1', '108.ec1', '108.ef1', '108.eg1', '576.v1'], 'core': '108.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [12138, 15624, 15984, 76, 10368, 15552, 2592, 5712], 'label': '31104.fx.36.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '36.bw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bw1', 'subgroup_fusion': None, 'weyl_group': '3456.di'}
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id: 186246259
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ns2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fq1', '216.cs1', '216.dh1', '216.di1'], 'contains': ['864.ey1', '864.ey2', '864.ez1', '864.ez3', '864.fe1', '864.fj1', '864.gj1', '1296.lc1', '1296.ld1', '1296.le1', '1296.le2'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [108, 12384, 16056, 432, 12096], 'label': '31104.fx.432.ns2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.dw1', 'old_label': '432.ns2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ns2', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 186246260
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.nt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ft1', '216.dj1', '216.kf1', '216.kp1', '216.ll1', '216.ly1', '216.md1', '216.mh1'], 'contains': ['864.fk1', '864.fu1', '864.gb1', '1296.lf1', '1296.lg1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1, 10368, 3024, 1728, 2592], 'label': '31104.fx.432.nt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.nt1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.nt1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 186246261
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.nu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.ct1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fr1', '144.fs1', '144.ft1', '216.dj1', '216.kg1', '216.lc1', '216.le1', '216.ls1', '216.mf1', '216.mi1'], 'contains': ['864.fk1', '864.fu1', '864.gc1', '1296.lf1', '1296.lg2'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1, 10368, 18576, 1728, 2592], 'label': '31104.fx.432.nu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.nu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.nu1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186246262
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.nv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ft1', '216.dk1', '216.kh1', '216.mj1'], 'contains': ['864.fl1', '864.ga1', '864.gj1', '1296.lf1', '1296.lh1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1, 12384, 18576, 1728, 2592], 'label': '31104.fx.432.nv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.p1', 'old_label': '432.nv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.nv1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246263
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.nw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.fo1', '144.fu1', '216.ju1', '216.ln1', '216.mc1'], 'contains': ['864.ge1', '1296.lg1', '1296.li1', '1296.lj1', '1728.dd1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1, 2592, 5712, 22752, 18576], 'label': '31104.fx.432.nw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.gd1', 'old_label': '432.nw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.nw1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186246264
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.nx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.fp1', '144.fr1', '144.fu1', '216.jv1', '216.lp1', '216.lz1'], 'contains': ['864.gf1', '1296.lg2', '1296.li1', '1728.de1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [1, 2592, 20812, 22752, 432], 'label': '31104.fx.432.nx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.di1', 'old_label': '432.nx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.nx1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
-
id: 186246265
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ny1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.fq1', '144.fs1', '144.fu1', '216.ma1'], 'contains': ['864.gg1', '1296.lg2', '1296.lj1', '1728.df1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [1, 2592, 28464, 10368, 18576], 'label': '31104.fx.432.ny1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.fe1', 'old_label': '432.ny1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ny1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
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id: 186246266
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.nz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ft1', '144.fu1', '216.dl1', '216.ke1', '216.ld1', '216.lo1', '216.lt1', '216.mb1', '216.mg1'], 'contains': ['864.fm1', '864.fy1', '864.gi1', '1296.lg1', '1296.lg2', '1296.lh1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1, 10368, 3024, 2592, 22752], 'label': '31104.fx.432.nz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '432.nz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.nz1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186246267
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.oa1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.fu1', '144.fu1', '216.jw1'], 'contains': ['864.gk1', '1296.lh1', '1296.li1', '1296.lj1', '1728.dj1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [1, 2592, 5712, 12384, 18576], 'label': '31104.fx.432.oa1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.jw1', 'old_label': '432.oa1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.oa1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186246268
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ob1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ob1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fv1', '216.ct1', '216.dm1', '216.ki1', '216.lc1', '216.lr1', '216.me1', '216.mk1'], 'contains': ['864.fn1', '864.gc1', '1296.lk1', '1296.lo1', '1296.lp1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [2179, 18576, 2592, 12096, 10368], 'label': '31104.fx.432.ob1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '432.ob1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ob1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 186246269
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.m1', '18.bd1'], 'contains': ['72.cv1', '108.a1', '108.ed1', '576.w1'], 'core': '108.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [17371, 16056, 18576, 29904, 22752, 15552, 18144, 15484], 'label': '31104.fx.36.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1', 'old_label': '36.bx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bx1', 'subgroup_fusion': None, 'weyl_group': '1728.46101'}
-
id: 186246270
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.oc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.gc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fv1', '216.cv1', '216.dn1', '216.kj1', '216.kp1', '216.lu1', '216.lx1', '216.ml1'], 'contains': ['864.fo1', '864.gb1', '1296.ll1', '1296.lo1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [17299, 22752, 2592, 12096, 18576], 'label': '31104.fx.432.oc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '432.oc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.oc1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
-
id: 186246271
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.od1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.gc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fv1', '216.cu1', '216.dn1', '216.do1', '216.kk1', '216.lv1', '216.mm1', '216.mm2'], 'contains': ['864.fp1', '864.gb1', '1296.ll1', '1296.lp1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1819, 22752, 18576, 12096, 2592], 'label': '31104.fx.432.od1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.s1', 'old_label': '432.od1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.od1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 186246272
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.oe1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ep1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fw1', '216.cx1', '216.dq1', '216.dr1', '216.kk1', '216.lj1', '216.ml1', '216.mm2'], 'contains': ['864.fs1', '864.gb1', '1296.lm1', '1296.lq1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [18150, 12096, 18576, 10368, 16056], 'label': '31104.fx.432.oe1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bb1', 'old_label': '432.oe1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.oe1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 186246273
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.oe2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ep1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fw1', '216.cy1', '216.dq1', '216.kj1', '216.ko1', '216.lj2', '216.ly1', '216.mm1'], 'contains': ['864.fr1', '864.gb1', '1296.lm1', '1296.lq2'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [25975, 12096, 2592, 22752, 18576], 'label': '31104.fx.432.oe2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '432.oe2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.oe2', 'subgroup_fusion': None, 'weyl_group': '96.209'}
-
id: 186246274
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.of1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.ll1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fw1', '216.da1', '216.ds1', '216.ki1', '216.kt1', '216.lb1', '216.ls1', '216.mk1'], 'contains': ['864.ft1', '864.gc1', '1296.ln1', '1296.lq1', '1296.lq2'], 'core': '10368.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [10855, 10368, 2592, 18576, 12096], 'label': '31104.fx.432.of1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '432.of1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.of1', 'subgroup_fusion': None, 'weyl_group': '144.154'}
-
id: 186246275
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.og1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.gc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fv1', '216.cw1', '216.du1', '216.kl1', '216.ld1', '216.lq1', '216.lw1', '216.mn1'], 'contains': ['864.fv1', '864.gi1', '1296.lk1', '1296.ll1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [2179, 22752, 2592, 10368, 18576], 'label': '31104.fx.432.og1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '432.og1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.og1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
-
id: 186246276
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.oh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ep1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fw1', '216.cz1', '216.dw1', '216.kl1', '216.la1', '216.lk1', '216.lt1', '216.mn1'], 'contains': ['864.fx1', '864.gi1', '1296.lm1', '1296.ln1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [10855, 10368, 2592, 22752, 18576], 'label': '31104.fx.432.oh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '432.oh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.oh1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
-
id: 186246277
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.oi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.a1', '144.fx1'], 'contains': ['864.gm1', '864.gn1', '864.hk1', '864.ht1', '864.ia1', '1296.lr1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [20737, 16080, 24198, 36, 30964], 'label': '31104.fx.432.oi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.oi1', 'old_label': '432.oi1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.oi1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 186246278
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.oj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.gd1', '144.fx1', '144.fz1'], 'contains': ['864.gp1', '864.gq1', '864.gt1', '864.hi1', '864.ho1', '864.hr1', '864.ie1', '1296.lr1', '1296.lt1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [5713, 10368, 6486, 36, 7276], 'label': '31104.fx.432.oj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.oj1', 'old_label': '432.oj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.oj1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 186246279
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ok1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.ge1', '144.fx1', '144.fy1', '144.fz1'], 'contains': ['864.go1', '864.gr1', '864.gu1', '864.hf1', '864.hv1', '864.hw1', '864.hx1', '1296.lr1', '1296.lt1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [5713, 22752, 6486, 36, 5260], 'label': '31104.fx.432.ok1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.ok1', 'old_label': '432.ok1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ok1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 186246280
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.o1', '18.bh1'], 'contains': ['72.ct1', '108.eh1', '108.el1', '108.eq1', '108.er1', '108.et1', '576.y1'], 'core': '648.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [6, 15624, 15984, 76, 28464, 15552, 2592, 10368], 'label': '31104.fx.36.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bh1', 'old_label': '36.by1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.by1', 'subgroup_fusion': None, 'weyl_group': '576.8654'}
-
id: 186246281
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.ol1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fy1', '144.ga1', '216.hw1'], 'contains': ['864.gy1', '864.gz1', '864.hc1', '864.he1', '864.hn1', '864.hq1', '864.if1', '1296.ls1', '1296.lt1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [5713, 10368, 6, 36, 12096], 'label': '31104.fx.432.ol1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.hw1', 'old_label': '432.ol1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ol1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 186246282
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.om1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.fz1', '144.ga1', '216.hy1'], 'contains': ['864.ha1', '864.hb1', '864.hj1', '864.hs1', '864.hz1', '1296.lt1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [5713, 10368, 24198, 36, 22752], 'label': '31104.fx.432.om1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.hy1', 'old_label': '432.om1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.om1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 186246283
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.on1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.gb1', '216.hw1'], 'contains': ['864.he1', '864.hh1', '864.hl1', '864.hn1', '864.hq1', '864.if1', '864.in1', '1296.lu1', '1296.lv1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [5713, 22752, 6, 18612, 12096], 'label': '31104.fx.432.on1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.hw1', 'old_label': '432.on1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.on1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 186246284
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '432.oo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.gb1', '216.hy1'], 'contains': ['864.hj1', '864.hm1', '864.hs1', '864.hz1', '864.ih1', '1296.lv1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [5713, 10368, 24198, 18612, 22752], 'label': '31104.fx.432.oo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.hy1', 'old_label': '432.oo1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.oo1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 186246285
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '486.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['162.a1', '162.b1', '162.d1', '243.a1'], 'contains': ['972.e1', '972.g1', '972.h1', '972.k1', '972.l1', '972.o1', '972.p1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [21265, 8646, 36], 'label': '31104.fx.486.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '486.a1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 186246286
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '486.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.c1', '162.e1', '243.a1'], 'contains': ['972.a1', '972.b1', '972.c1', '972.d1', '972.e1', '972.f1', '972.i1', '972.m1', '972.q1', '972.bf1', '972.bg1', '972.bh1', '972.bi1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [5713, 24198, 36, 2592, 16056], 'label': '31104.fx.486.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '486.b1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.b1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 186246287
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '486.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.f1', '162.g1', '243.a1'], 'contains': ['972.f1', '972.g1', '972.s1', '972.u1', '972.v1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [5713, 8646, 36], 'label': '31104.fx.486.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '486.c1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.c1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 186246288
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '486.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['162.h1', '162.i1', '162.k1', '243.a1'], 'contains': ['972.i1', '972.j1', '972.l1', '972.n1', '972.p1', '972.r1', '972.s1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [21265, 8646, 15588], 'label': '31104.fx.486.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '486.d1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.d1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 186246289
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '486.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.j1', '162.l1', '243.a1'], 'contains': ['972.j1', '972.k1', '972.m1', '972.t1', '972.v1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [5713, 8646, 15588], 'label': '31104.fx.486.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '486.e1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.e1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 186246290
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '486.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.m1', '162.n1', '243.a1'], 'contains': ['972.n1', '972.o1', '972.q1', '972.t1', '972.u1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [5713, 24198, 15588], 'label': '31104.fx.486.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '486.f1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.f1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 186246291
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.o1', '18.h1', '18.v1', '18.bi1'], 'contains': ['72.cu1', '108.eh1', '108.ej1', '108.ep1', '108.es1', '576.z1'], 'core': '216.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [6, 15624, 15984, 76, 5712, 15552, 2592, 10368], 'label': '31104.fx.36.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.bz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bz1', 'subgroup_fusion': None, 'weyl_group': '1152.157852'}
-
id: 186246292
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '486.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cm1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['162.o1', '162.p1', '162.s1', '162.t1', '162.u1', '243.a1'], 'contains': ['972.e1', '972.g1', '972.j1', '972.n1', '972.ba1', '972.bb1', '972.bc1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [24198, 36, 18144, 15552], 'label': '31104.fx.486.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '486.g1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.g1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
-
id: 186246293
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '486.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.q1', '162.r1', '162.v1', '162.w1', '162.x1', '243.a1'], 'contains': ['972.f1', '972.h1', '972.r1', '972.t1', '972.w1', '972.x1', '972.y1', '972.z1', '972.ba1', '972.bd1', '972.be1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [20737, 36, 16056, 18576], 'label': '31104.fx.486.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '486.h1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.h1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 186246294
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '486.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ct1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['162.y1', '162.z1', '162.ba1', '162.bb1', '162.bd1', '162.be1', '243.a1'], 'contains': ['972.i1', '972.k1', '972.o1', '972.s1', '972.bb1', '972.bc1', '972.bd1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [7477, 6, 15552], 'label': '31104.fx.486.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '486.i1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.i1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 186246295
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '486.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cv1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.bc1', '162.bf1', '162.bg1', '243.a1'], 'contains': ['972.l1', '972.m1', '972.u1', '972.bb1', '972.be1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [5713, 12138, 15552], 'label': '31104.fx.486.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '486.j1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.j1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 186246296
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '486.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.bh1', '162.bi1', '162.bj1', '162.bk1', '243.a1'], 'contains': ['972.p1', '972.q1', '972.v1', '972.bc1', '972.be1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [5713, 6, 15552], 'label': '31104.fx.486.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '486.k1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.k1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 186246297
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': ['54.cb1', '54.ca1', '54.cc1', '54.bz1', '54.bl1', '54.bs1', '54.bt1'], 'conjugacy_class_count': 1, 'contained_in': ['192.c1', '192.d1', '288.e1', '288.cb1', '288.dg1', '288.dh1'], 'contains': ['1152.a1', '1728.z1', '1728.ba1', '1728.bb1'], 'core': '576.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [36, 12096, 22752, 10368], 'label': '31104.fx.576.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '576.a1', 'normal_contained_in': ['36.a1'], 'normal_contains': ['1152.a1'], 'normalizer': '1.a1', 'old_label': '576.a1', 'projective_image': '31104.fx', 'quotient_action_image': '36.10', 'quotient_action_kernel': '16.14', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '576.a1', 'subgroup_fusion': None, 'weyl_group': '1944.2342'}
-
id: 186246298
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.a1', '288.a1', '288.e1', '288.f1', '288.m1', '288.n1', '288.o1', '288.p1', '288.t1', '288.u1', '288.bb1', '288.bi1'], 'contains': ['1152.a1', '1728.a1', '1728.d1', '1728.e1', '1728.f1', '1728.g1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [18144, 12096, 10368, 2016], 'label': '31104.fx.576.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '576.b1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 186246299
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.db1', '192.a1', '288.b1', '288.g1', '288.j1', '288.s1', '288.v1', '288.w1', '288.bj1'], 'contains': ['1152.h1', '1728.b1', '1728.d1', '1728.h1', '1728.i1', '1728.j1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [3096, 10924, 10368, 12384], 'label': '31104.fx.576.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.d1', 'old_label': '576.c1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.c1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 186246300
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dc1', '192.a1', '288.h1', '288.x1', '288.bm1'], 'contains': ['1152.j1', '1728.c1', '1728.d1', '1728.k1', '1728.l1', '1728.m1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [18144, 10368, 11764, 2016], 'label': '31104.fx.576.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.i1', 'old_label': '576.d1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 186246301
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.df1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dd1', '192.a1', '288.c1', '288.i1', '288.k1', '288.q1', '288.y1', '288.z1', '288.bp1'], 'contains': ['1152.l1', '1728.e1', '1728.i1', '1728.k1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [18648, 556, 12096, 12384], 'label': '31104.fx.576.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.d1', 'old_label': '576.e1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.e1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 186246302
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.n1', '12.o1', '12.p1', '18.l1', '18.ba1', '18.bj1'], 'contains': ['72.b1', '108.eh1', '108.ek1', '108.em1', '108.eo1', '144.fb1'], 'core': '72.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [6, 18576, 2592, 76, 2664, 22752, 15552, 10368], 'label': '31104.fx.36.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.ca1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ca1', 'subgroup_fusion': None, 'weyl_group': '1152.155790'}
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id: 186246303
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.df1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.de1', '192.a1', '288.d1', '288.l1', '288.bp1'], 'contains': ['1152.l1', '1728.f1', '1728.i1', '1728.l1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [3096, 556, 12096, 12384], 'label': '31104.fx.576.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.f1', 'old_label': '576.f1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.f1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
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id: 186246304
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.df1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.df1', '192.a1', '288.r1', '288.ba1', '288.br1'], 'contains': ['1152.m1', '1728.e1', '1728.j1', '1728.l1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [18648, 12096, 10924, 12384], 'label': '31104.fx.576.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.q1', 'old_label': '576.g1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.g1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
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id: 186246305
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.df1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dg1', '192.a1', '288.br1'], 'contains': ['1152.m1', '1728.f1', '1728.j1', '1728.k1', '1728.l1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [3096, 12096, 10924, 12384], 'label': '31104.fx.576.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.g1', 'old_label': '576.h1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.h1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
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id: 186246306
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.a1', '288.bb1', '288.cb1', '288.cc1', '288.cd1', '288.ce1', '288.cf1', '288.cg1', '288.ch1', '288.ci1', '288.cj1', '288.ck1', '288.cl1', '288.cm1', '288.cr1'], 'contains': ['1152.a1', '1728.n1', '1728.o1', '1728.p1', '1728.q1', '1728.r1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [16056, 12096, 22752, 10368], 'label': '31104.fx.576.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '576.i1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.i1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186246307
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.r1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.bh1', '192.b1', '288.cu1', '288.cv1', '288.cw1'], 'contains': ['1152.e1', '1728.s1', '1728.t1', '1728.u1', '1728.v1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [36, 10228, 16080, 10368], 'label': '31104.fx.576.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fx1', 'old_label': '576.j1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.j1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246308
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.r1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bi1', '144.bj1', '192.b1', '288.cx1'], 'contains': ['1152.p1', '1728.s1', '1728.w1', '1728.x1', '1728.y1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [36, 18580, 16080, 12384], 'label': '31104.fx.576.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.cx1', 'old_label': '576.k1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.k1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186246309
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.bk1', '144.ep1', '144.eq1', '192.d1', '288.cy1', '288.da1', '288.de1'], 'contains': ['1152.b1', '1728.v1', '1728.z1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [36, 5712, 12096, 10368], 'label': '31104.fx.576.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fy1', 'old_label': '576.l1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.l1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
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id: 186246310
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ea1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bm1', '192.b1', '192.c1', '288.b1', '288.dc1'], 'contains': ['1152.h1', '1728.t1', '1728.w1', '1728.x1', '1728.ba1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [36, 10924, 2016, 10368], 'label': '31104.fx.576.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1', 'old_label': '576.m1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.m1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
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id: 186246311
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.r1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.bn1', '144.er1', '192.b1', '192.d1', '288.cz1', '288.db1', '288.dd1'], 'contains': ['1152.i1', '1728.u1', '1728.v1', '1728.y1', '1728.ba1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [36, 76, 12384, 10368], 'label': '31104.fx.576.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bc1', 'old_label': '576.n1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.n1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186246312
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bp1', '192.c1', '288.c1', '288.d1', '288.df1'], 'contains': ['1152.l1', '1728.x1', '1728.bb1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [36, 556, 12096, 12384], 'label': '31104.fx.576.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bn1', 'old_label': '576.o1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.o1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
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id: 186246313
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.d1', '18.m1', '18.u1', '18.bk1'], 'contains': ['72.cr1', '108.ei1', '108.ej1', '108.en1', '144.fc1', '144.fd1'], 'core': '216.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [6, 16056, 432, 5712, 10368, 15552, 18144, 12096], 'label': '31104.fx.36.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.cb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cb1', 'subgroup_fusion': None, 'weyl_group': '1152.155790'}
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id: 186246314
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.et1', '192.e1', '288.cy1', '288.di1', '288.dt1'], 'contains': ['1152.b1', '1728.bc1', '1728.bd1', '1728.be1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [14802, 20812, 12096, 22752], 'label': '31104.fx.576.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fy1', 'old_label': '576.p1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.p1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246315
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.br1', '192.g1', '288.cu1', '288.dj1', '288.du1'], 'contains': ['1152.e1', '1728.bd1', '1728.bg1', '1728.bk1', '1728.bl1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [12138, 8212, 22752, 5712], 'label': '31104.fx.576.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fx1', 'old_label': '576.q1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.q1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246316
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.gc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.e1', '192.f1', '288.cc1', '288.dg1', '288.dk1', '288.dn1', '288.do1'], 'contains': ['1152.a1', '1728.bc1', '1728.bf1', '1728.bj1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [17371, 12096, 10368, 22752], 'label': '31104.fx.576.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.x1', 'old_label': '576.r1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.r1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186246317
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ew1', '192.e1', '192.g1', '288.cz1', '288.dl1', '288.dv1'], 'contains': ['1152.i1', '1728.bd1', '1728.bh1', '1728.bj1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [17371, 5712, 10368, 22752], 'label': '31104.fx.576.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bd1', 'old_label': '576.s1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.s1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186246318
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ex1', '192.e1', '192.h1', '288.dm1'], 'contains': ['1152.k1', '1728.be1', '1728.bi1', '1728.bj1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [17371, 29904, 10368, 22752], 'label': '31104.fx.576.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.u1', 'old_label': '576.t1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.t1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246319
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ey1', '144.ez1', '192.f1', '288.da1', '288.dq1', '288.dt1'], 'contains': ['1152.b1', '1728.bf1', '1728.bm1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [12138, 12096, 5712, 10368], 'label': '31104.fx.576.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bd1', 'old_label': '576.u1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.u1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
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id: 186246320
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.bw1', '192.g1', '288.cv1', '288.dr1', '288.du1'], 'contains': ['1152.e1', '1728.bh1', '1728.bk1', '1728.bl1', '1728.bm1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [17371, 8304, 23836, 22752], 'label': '31104.fx.576.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bc1', 'old_label': '576.v1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.v1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186246321
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.bx1', '192.h1', '288.ds1'], 'contains': ['1152.f1', '1728.bi1', '1728.bm1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [12138, 6484, 16080, 10368], 'label': '31104.fx.576.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.x1', 'old_label': '576.w1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.w1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
-
id: 186246322
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fa1', '192.f1', '192.g1', '192.h1', '288.db1', '288.dp1', '288.dv1'], 'contains': ['1152.i1', '1728.bg1', '1728.bj1', '1728.bm1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [12138, 22752, 5712, 10368], 'label': '31104.fx.576.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.d1', 'old_label': '576.x1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.x1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
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id: 186246323
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.by1', '192.j1', '288.dw1'], 'contains': ['1152.d1', '1728.bn1', '1728.br1', '1728.bw1', '1728.bx1', '1728.bz1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 576, 'diagramx': None, 'generators': [26047, 8304, 22752, 3100], 'label': '31104.fx.576.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.dw1', 'old_label': '576.y1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.y1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186246324
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.n1', '18.k1', '18.bb1', '18.bk1'], 'contains': ['72.cr1', '108.ek1', '108.eu1', '144.fj1'], 'core': '216.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [26047, 2592, 15552, 5712, 15984, 10368, 12096, 15624], 'label': '31104.fx.36.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '36.cc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cc1', 'subgroup_fusion': None, 'weyl_group': '3456.gu'}
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id: 186246325
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.bz1', '192.j1', '288.cv1', '288.dj1', '288.dx1'], 'contains': ['1152.e1', '1728.bn1', '1728.bp1', '1728.bv1', '1728.by1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [6, 18580, 10368, 5712], 'label': '31104.fx.576.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fx1', 'old_label': '576.z1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.z1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246326
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fb1', '192.i1', '192.j1', '192.k1', '288.cz1', '288.dp1', '288.dy1'], 'contains': ['1152.i1', '1728.bn1', '1728.bq1', '1728.bs1', '1728.bu1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [2670, 76, 10368, 22752], 'label': '31104.fx.576.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fz1', 'old_label': '576.ba1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.ba1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186246327
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fc1', '144.fd1', '192.l1', '288.da1', '288.di1', '288.dz1'], 'contains': ['1152.b1', '1728.bo1', '1728.bp1', '1728.bt1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [26047, 23836, 12096, 22752], 'label': '31104.fx.576.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fy1', 'old_label': '576.bb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.bb1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246328
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fj1', '192.i1', '288.cy1', '288.dq1', '288.dz1'], 'contains': ['1152.b1', '1728.bq1', '1728.ca1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [26047, 5712, 12096, 10368], 'label': '31104.fx.576.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bd1', 'old_label': '576.bc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.bc1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
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id: 186246329
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fe1', '144.ff1', '192.l1', '288.ea1'], 'contains': ['1152.c1', '1728.bo1', '1728.br1', '1728.bt1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 576, 'diagramx': None, 'generators': [6, 28464, 12096, 10368], 'label': '31104.fx.576.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.ea1', 'old_label': '576.bd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.bd1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246330
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fk1', '192.i1', '288.ea1'], 'contains': ['1152.c1', '1728.bs1', '1728.ca1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [26047, 28464, 12096, 10368], 'label': '31104.fx.576.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.bb1', 'old_label': '576.be1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.be1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
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id: 186246331
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.cf1', '192.j1', '288.dw1'], 'contains': ['1152.d1', '1728.bs1', '1728.bw1', '1728.by1', '1728.bz1', '1728.cb1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [26047, 31056, 3100, 10368], 'label': '31104.fx.576.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.ba1', 'old_label': '576.bf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.bf1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
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id: 186246332
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.cg1', '192.j1', '288.cu1', '288.dr1', '288.dx1'], 'contains': ['1152.e1', '1728.bq1', '1728.bv1', '1728.bx1', '1728.cb1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [6, 8212, 5712, 22752], 'label': '31104.fx.576.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bc1', 'old_label': '576.bg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.bg1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186246333
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.ch1', '192.k1', '288.ds1'], 'contains': ['1152.f1', '1728.bq1', '1728.cc1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [6, 16564, 19536, 22752], 'label': '31104.fx.576.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.x1', 'old_label': '576.bh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.bh1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
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id: 186246334
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.ci1', '192.k1'], 'contains': ['1152.g1', '1728.bs1', '1728.cc1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 384, 'diagramx': None, 'generators': [6, 26932, 19536, 22752], 'label': '31104.fx.576.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '192.k1', 'old_label': '576.bi1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.bi1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
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id: 186246335
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '6.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1'], 'contains': ['12.f1', '12.g1', '12.h1', '12.i1', '12.k1', '12.q1', '12.v1', '18.o1', '18.r1', '18.t1', '24.d1'], 'core': '36.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1, 18216, 10924, 12096, 18144, 36, 15552, 12384, 10368, 18576], 'label': '31104.fx.6.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '6.f1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.f1', 'subgroup_fusion': None, 'weyl_group': None}
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id: 186246336
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.d1', '18.bl1'], 'contains': ['72.cs1', '108.ei1', '108.el1', '108.en1', '144.fe1', '144.ff1'], 'core': '648.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [26047, 16056, 18576, 3100, 22752, 15552, 2592, 12096], 'label': '31104.fx.36.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bl1', 'old_label': '36.cd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cd1', 'subgroup_fusion': None, 'weyl_group': '576.5126'}
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id: 186246337
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ep1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.i1', '192.l1', '288.cd1', '288.dg1', '288.dk1', '288.dn1', '288.eb1'], 'contains': ['1152.a1', '1728.bo1', '1728.bu1', '1728.ca1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [6, 10368, 12096, 22752], 'label': '31104.fx.576.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.x1', 'old_label': '576.bj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.bj1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
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id: 186246338
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fh1', '192.j1', '192.l1', '288.db1', '288.dl1', '288.dy1'], 'contains': ['1152.i1', '1728.bp1', '1728.br1', '1728.bu1', '1728.cb1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [26047, 22752, 3100, 10368], 'label': '31104.fx.576.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bc1', 'old_label': '576.bk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.bk1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186246339
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fi1', '192.k1', '192.l1', '288.dm1'], 'contains': ['1152.k1', '1728.bt1', '1728.bu1', '1728.cc1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [26047, 22752, 4540, 10368], 'label': '31104.fx.576.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.x1', 'old_label': '576.bl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.bl1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
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id: 186246340
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.m1', '192.n1', '288.f1', '288.ce1', '288.dh1', '288.dk1', '288.ed1', '288.ee1'], 'contains': ['1152.a1', '1728.cd1', '1728.ce1', '1728.ck1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [10405, 22752, 10368, 1728], 'label': '31104.fx.576.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.c1', 'old_label': '576.bm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.bm1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246341
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bt1', '192.m1', '192.o1', '192.p1', '288.g1', '288.dc1', '288.ec1'], 'contains': ['1152.h1', '1728.cd1', '1728.cf1', '1728.cl1', '1728.cm1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [10405, 22752, 10368, 12940], 'label': '31104.fx.576.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.f1', 'old_label': '576.bn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.bn1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 186246342
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.bu1', '144.fn1', '192.n1', '192.p1', '192.q1', '288.dd1', '288.dl1', '288.dp1'], 'contains': ['1152.i1', '1728.cd1', '1728.cg1', '1728.ch1', '1728.cn1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [10405, 22752, 10368, 16080], 'label': '31104.fx.576.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fz1', 'old_label': '576.bo1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.bo1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186246343
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bw1', '192.m1', '192.o1', '192.q1', '288.h1'], 'contains': ['1152.j1', '1728.cd1', '1728.ci1', '1728.co1', '1728.co2'], 'core': '3456.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [10405, 22752, 10368, 29404], 'label': '31104.fx.576.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.h1', 'old_label': '576.bp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.bp1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186246344
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.bx1', '144.fo1', '192.n1', '192.o1', '192.q1', '288.dm1'], 'contains': ['1152.k1', '1728.cd1', '1728.cj1', '1728.cj2', '1728.cp1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 576, 'diagramx': None, 'generators': [10405, 10368, 22752, 9168], 'label': '31104.fx.576.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.dm1', 'old_label': '576.bq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.bq1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186246345
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.bj1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.by1', '144.fp1', '192.n1', '288.de1', '288.di1', '288.dq1'], 'contains': ['1152.b1', '1728.ce1', '1728.ch1', '1728.cj1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [10405, 16080, 1728, 10368], 'label': '31104.fx.576.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bd1', 'old_label': '576.br1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.br1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246346
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.bz1', '192.p1', '288.cw1', '288.dj1', '288.dr1'], 'contains': ['1152.e1', '1728.cf1', '1728.cg1', '1728.ch1', '1728.cq1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [10405, 10368, 30964, 16080], 'label': '31104.fx.576.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bc1', 'old_label': '576.bs1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.bs1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186246347
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.n1', '18.bl1'], 'contains': ['72.cs1', '108.em1', '108.eu1', '144.fk1'], 'core': '648.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [6, 2592, 15552, 76, 18576, 22752, 12096, 2664], 'label': '31104.fx.36.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1', 'old_label': '36.ce1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ce1', 'subgroup_fusion': None, 'weyl_group': '1728.12469'}
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id: 186246348
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ca1', '192.q1', '288.ds1'], 'contains': ['1152.f1', '1728.ch1', '1728.ci1', '1728.cj2'], 'core': '10368.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [10405, 6484, 16080, 10368], 'label': '31104.fx.576.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.x1', 'old_label': '576.bt1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.bt1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246349
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cc1', '192.m1', '288.i1', '288.df1', '288.ef1'], 'contains': ['1152.l1', '1728.ck1', '1728.cm1', '1728.co2'], 'core': '31104.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [10405, 12940, 1728, 12384], 'label': '31104.fx.576.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.a1', 'old_label': '576.bu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.bu1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246350
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cd1', '144.cf1', '192.o1'], 'contains': ['1152.o1', '1728.cm1', '1728.co1', '1728.cp1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [10405, 6484, 9168, 12384], 'label': '31104.fx.576.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '192.o1', 'old_label': '576.bv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.bv1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 186246351
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ce1', '144.cg1', '192.p1', '288.cx1'], 'contains': ['1152.p1', '1728.cl1', '1728.cm1', '1728.cn1', '1728.cq1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [10405, 12384, 30964, 16080], 'label': '31104.fx.576.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.p1', 'old_label': '576.bw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.bw1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
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id: 186246352
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ck1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ch1', '192.r1', '288.b1', '288.j1', '288.ec1'], 'contains': ['1152.h1', '1728.cr1', '1728.cs1', '1728.ct1', '1728.cv1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [3132, 10924, 2016, 10368], 'label': '31104.fx.576.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bj1', 'old_label': '576.bx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.bx1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
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id: 186246353
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ci1', '192.r1', '288.c1', '288.l1', '288.ef1'], 'contains': ['1152.l1', '1728.ct1', '1728.cw1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [18684, 556, 12096, 12384], 'label': '31104.fx.576.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bn1', 'old_label': '576.by1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.by1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
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id: 186246354
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.by2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ci2', '192.r1', '288.d1', '288.k1', '288.l1'], 'contains': ['1152.l1', '1728.ct1', '1728.cw2'], 'core': '31104.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [15588, 556, 12096, 12384], 'label': '31104.fx.576.by2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.bo1', 'old_label': '576.by2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.by2', 'subgroup_fusion': None, 'weyl_group': '54.5'}
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id: 186246355
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.r1', '288.e1', '288.m1', '288.n1', '288.cf1', '288.cg1', '288.ed1'], 'contains': ['1152.a1', '1728.cu1', '1728.cv1', '1728.cw1', '1728.cw2', '1728.cw3'], 'core': '1152.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [18180, 12096, 22752, 10368], 'label': '31104.fx.576.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '576.bz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.bz1', 'subgroup_fusion': None, 'weyl_group': '324.124'}
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id: 186246356
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.m1', '288.o1', '288.cb1', '288.cf1', '288.ch1', '288.dn1', '288.ee1'], 'contains': ['1152.a1', '1728.cx1', '1728.cx2', '1728.cy1', '1728.cz1', '1728.cz2'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [16092, 12096, 22752, 10368], 'label': '31104.fx.576.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '576.ca1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.ca1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
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id: 186246357
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ck1', '144.fr1', '192.t1', '288.de1', '288.dt1', '288.dz1'], 'contains': ['1152.b1', '1728.da1', '1728.de1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [1, 12096, 5712, 10368], 'label': '31104.fx.576.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fy1', 'old_label': '576.cb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.cb1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
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id: 186246358
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.o1', '18.bh1'], 'contains': ['72.ct1', '108.em1', '108.eq1', '108.es1', '108.et1', '108.ev1', '576.bf1'], 'core': '648.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [6, 15624, 15984, 76, 22752, 15552, 2592, 5712], 'label': '31104.fx.36.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.m1', 'old_label': '36.cf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cf1', 'subgroup_fusion': None, 'weyl_group': '1728.47856'}
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id: 186246359
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.cl1', '144.fs1', '192.t1', '288.ea1'], 'contains': ['1152.c1', '1728.da1', '1728.df1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 576, 'diagramx': None, 'generators': [1, 12096, 28464, 10368], 'label': '31104.fx.576.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.ea1', 'old_label': '576.cc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.cc1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
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id: 186246360
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.s1', '192.t1', '288.p1', '288.ci1', '288.dh1', '288.do1', '288.eb1', '288.ed1', '288.ee1'], 'contains': ['1152.a1', '1728.da1', '1728.db1', '1728.dg1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1, 12096, 22752, 10368], 'label': '31104.fx.576.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.c1', 'old_label': '576.cd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.cd1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186246361
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.co1', '192.s1', '288.q1', '288.df1', '288.ef1'], 'contains': ['1152.l1', '1728.db1', '1728.di1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [1, 1728, 556, 12384], 'label': '31104.fx.576.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.g1', 'old_label': '576.ce1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.ce1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
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id: 186246362
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cq1', '192.s1', '288.r1'], 'contains': ['1152.m1', '1728.db1', '1728.dk1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [1, 1728, 10924, 12384], 'label': '31104.fx.576.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.r1', 'old_label': '576.cf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.cf1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
-
id: 186246363
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.cr1', '192.u1', '288.dw1'], 'contains': ['1152.d1', '1728.dc1', '1728.dd1', '1728.df1', '1728.dl1', '1728.dm1', '1728.do1', '1728.dp1', '1728.dr1', '1728.dr2'], 'core': '10368.a1', 'coset_action_label': None, 'count': 576, 'diagramx': None, 'generators': [1, 18580, 28464, 10368], 'label': '31104.fx.576.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.dw1', 'old_label': '576.cg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.cg1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
-
id: 186246364
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.cs1', '192.u1', '288.cw1', '288.du1', '288.dx1'], 'contains': ['1152.e1', '1728.dc1', '1728.dd1', '1728.de1', '1728.dl1', '1728.dn1', '1728.dp1', '1728.dq1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [1, 18580, 5712, 10368], 'label': '31104.fx.576.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fx1', 'old_label': '576.ch1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.ch1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
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id: 186246365
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cu1', '192.s1', '192.u1', '288.s1', '288.dc1', '288.ec1'], 'contains': ['1152.h1', '1728.dc1', '1728.dg1', '1728.dh1', '1728.di1', '1728.dk1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [1, 10924, 22752, 12384], 'label': '31104.fx.576.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.a1', 'old_label': '576.ci1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.ci1', 'subgroup_fusion': None, 'weyl_group': '324.124'}
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id: 186246366
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.cv1', '144.fu1', '192.t1', '192.u1', '288.dd1', '288.dv1', '288.dy1'], 'contains': ['1152.i1', '1728.dd1', '1728.de1', '1728.df1', '1728.dg1', '1728.dj1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [1, 5712, 22752, 10368], 'label': '31104.fx.576.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bd1', 'old_label': '576.cj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.cj1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
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id: 186246367
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cw1', '144.cx1', '192.u1'], 'contains': ['1152.n1', '1728.dh1', '1728.dj1', '1728.dk1', '1728.dl1', '1728.dm1', '1728.dp1', '1728.dq1', '1728.dr1', '1728.dr2'], 'core': '31104.a1', 'coset_action_label': None, 'count': 576, 'diagramx': None, 'generators': [1, 18580, 5712, 12384], 'label': '31104.fx.576.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '576.ck1', 'old_label': '576.ck1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.ck1', 'subgroup_fusion': None, 'weyl_group': '54.14'}
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id: 186246368
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '576.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cy1', '144.cz1', '192.u1', '288.cx1'], 'contains': ['1152.p1', '1728.dh1', '1728.di1', '1728.dj1', '1728.dl1', '1728.dm1', '1728.dn1', '1728.do1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [1, 8212, 5712, 12384], 'label': '31104.fx.576.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.cx1', 'old_label': '576.cl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.cl1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
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id: 186246369
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.o1', '18.g1', '18.bc1', '18.bi1'], 'contains': ['72.cu1', '108.ek1', '108.ep1', '108.er1', '108.ev1', '576.bg1'], 'core': '216.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [6, 15624, 15984, 20812, 22752, 15552, 2592, 5712], 'label': '31104.fx.36.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '36.cg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cg1', 'subgroup_fusion': None, 'weyl_group': '3456.di'}
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id: 186246370
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['216.a1', '216.b1', '216.gw1', '216.gx1', '216.gy1', '216.gz1', '216.ha1', '216.hb1', '216.hb2', '324.dg1', '324.dj1', '324.dn1', '324.dp1', '324.ds1', '324.dx1', '324.ef1'], 'contains': ['1296.ed1', '1296.fo1', '1944.a1'], 'core': '648.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [16056, 22752, 18576, 18144, 15552], 'label': '31104.fx.648.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '648.a1', 'normal_contained_in': ['216.a1', '216.b1'], 'normal_contains': ['1944.a1', '10368.a1'], 'normalizer': '1.a1', 'old_label': '648.a1', 'projective_image': '31104.fx', 'quotient_action_image': '72.46', 'quotient_action_kernel': '9.2', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '648.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186246371
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.c1', '216.d1', '324.cm1'], 'contains': ['1296.a1', '1296.h1', '1296.ba1', '1296.bf1', '1296.bj1', '1296.bt1', '1296.ck1', '1944.b1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [20737, 22752, 36, 16056, 15552], 'label': '31104.fx.648.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cm1', 'old_label': '648.b1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246372
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.c1', '216.e1', '324.co1'], 'contains': ['1296.b1', '1296.i1', '1296.bb1', '1296.bg1', '1296.bk1', '1296.bu1', '1296.cl1', '1944.b1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [20737, 12384, 36, 16056, 15552], 'label': '31104.fx.648.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.co1', 'old_label': '648.c1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.c1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186246373
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.c1', '216.f1', '324.cn1'], 'contains': ['1296.c1', '1296.j1', '1296.bc1', '1296.bh1', '1296.bl1', '1296.bv1', '1296.cm1', '1944.b1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [20737, 12384, 36, 2664, 18144], 'label': '31104.fx.648.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cn1', 'old_label': '648.d1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.d1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246374
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.d1', '216.e1', '216.f1', '324.cp1'], 'contains': ['1296.f1', '1296.k1', '1296.z1', '1296.bi1', '1296.bm1', '1296.bz1', '1296.cj1', '1944.b1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [20737, 1728, 36, 16056, 15552], 'label': '31104.fx.648.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cp1', 'old_label': '648.e1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.e1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246375
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.g1', '216.h1', '324.cm1'], 'contains': ['1296.h1', '1296.s1', '1296.ba1', '1296.bn1', '1296.bq1', '1296.cb1', '1296.cg1', '1944.c1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [1, 10368, 2628, 16056, 15552], 'label': '31104.fx.648.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cm1', 'old_label': '648.f1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.f1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246376
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.g1', '216.i1', '324.co1'], 'contains': ['1296.i1', '1296.t1', '1296.bb1', '1296.bo1', '1296.br1', '1296.cc1', '1296.ch1', '1944.c1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [20737, 12384, 2628, 16056, 15552], 'label': '31104.fx.648.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.co1', 'old_label': '648.g1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.g1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186246377
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.g1', '216.j1', '324.cn1'], 'contains': ['1296.j1', '1296.u1', '1296.bc1', '1296.bp1', '1296.bs1', '1296.cd1', '1296.ci1', '1944.c1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [20737, 12384, 15588, 2664, 18144], 'label': '31104.fx.648.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cn1', 'old_label': '648.h1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.h1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246378
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.h1', '216.i1', '216.j1', '324.cp1'], 'contains': ['1296.k1', '1296.x1', '1296.z1', '1296.bx1', '1296.by1', '1296.ce1', '1296.cf1', '1944.c1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [20737, 1728, 2628, 16056, 15552], 'label': '31104.fx.648.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cp1', 'old_label': '648.i1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.i1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186246379
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cr1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.k1', '216.n1', '324.c1', '324.d1', '324.i1'], 'contains': ['1296.cn1', '1296.cs1', '1296.cx1', '1296.fx1', '1296.ge1', '1296.gu1', '1296.ib1', '1944.d1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [29503, 10368, 36, 18648, 18576], 'label': '31104.fx.648.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.j1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.j1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186246380
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.p1', '18.bd1'], 'contains': ['72.cv1', '108.ek1', '108.ew1', '576.bh1'], 'core': '216.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [26047, 16056, 18576, 5712, 10368, 15552, 18144, 4540], 'label': '31104.fx.36.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1', 'old_label': '36.ch1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ch1', 'subgroup_fusion': None, 'weyl_group': '1728.46101'}
-
id: 186246381
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.ct1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.k1', '216.l1', '324.a1', '324.b1', '324.j1'], 'contains': ['1296.cp1', '1296.ct1', '1296.cy1', '1296.fy1', '1296.gi1', '1296.gv1', '1296.ic1', '1944.d1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [26047, 12096, 36, 18648, 18576], 'label': '31104.fx.648.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '648.k1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.k1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186246382
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.k1', '216.m1', '324.k1'], 'contains': ['1296.cr1', '1296.cu1', '1296.cz1', '1296.fz1', '1296.gj1', '1296.gw1', '1296.id1', '1944.d1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [26047, 12096, 36, 15552, 2592], 'label': '31104.fx.648.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.k1', 'old_label': '648.l1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.l1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186246383
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cr1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.l1', '216.m1', '216.n1', '324.c1', '324.d1', '324.l1'], 'contains': ['1296.cn1', '1296.cv1', '1296.cw1', '1296.ga1', '1296.gf1', '1296.hm1', '1296.hu1', '1944.d1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [19135, 22752, 36, 18648, 18576], 'label': '31104.fx.648.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.m1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.m1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186246384
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.q1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.o1', '216.p1', '324.c1', '324.m1', '324.cm1'], 'contains': ['1296.bf1', '1296.bn1', '1296.cn1', '1296.da1', '1296.do1', '1296.gb1', '1296.ir1', '1944.e1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1, 10368, 36, 15552, 2592], 'label': '31104.fx.648.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '648.n1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.n1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
-
id: 186246385
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.o1', '216.q1', '324.n1', '324.cn1', '324.co1'], 'contains': ['1296.bg1', '1296.bh1', '1296.bo1', '1296.bp1', '1296.co1', '1296.db1', '1296.dp1', '1296.gc1', '1296.is1', '1944.e1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [20737, 12384, 36, 18144, 15552], 'label': '31104.fx.648.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.w1', 'old_label': '648.o1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.o1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186246386
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.p1', '216.q1', '324.a1', '324.o1', '324.cp1'], 'contains': ['1296.bi1', '1296.bx1', '1296.cp1', '1296.dc1', '1296.dn1', '1296.gd1', '1296.ix1', '1944.e1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [20737, 1728, 36, 15552, 2592], 'label': '31104.fx.648.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '648.p1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.p1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
-
id: 186246387
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.u1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.r1', '216.t1', '324.d1', '324.m1', '324.cq1'], 'contains': ['1296.cn1', '1296.dq1', '1296.ds1', '1296.gg1', '1296.ja1', '1944.f1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [433, 10368, 36, 18144, 2592], 'label': '31104.fx.648.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '648.q1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.q1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
-
id: 186246388
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.v1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.s1', '216.u1', '324.r1', '324.cm1', '324.cq1'], 'contains': ['1296.bj1', '1296.cb1', '1296.cn1', '1296.dr1', '1296.dt1', '1944.g1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [16057, 10368, 36, 2592, 15552], 'label': '31104.fx.648.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.v1', 'old_label': '648.r1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.r1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186246389
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.t1', '216.v1', '324.n1', '324.cr1', '324.cs1'], 'contains': ['1296.co1', '1296.du1', '1296.dx1', '1296.gh1', '1296.jb1', '1944.f1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [8209, 12384, 36, 15552, 2592], 'label': '31104.fx.648.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.w1', 'old_label': '648.s1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.s1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186246390
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.u1', '216.w1', '324.s1', '324.co1', '324.cr1'], 'contains': ['1296.bk1', '1296.cc1', '1296.co1', '1296.dv1', '1296.dy1', '1944.g1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [5689, 12384, 36, 18144, 15552], 'label': '31104.fx.648.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.w1', 'old_label': '648.t1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.t1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186246391
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.p1'], 'contains': ['72.cw1', '108.em1', '108.ew1', '576.bi1'], 'core': '648.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [6, 16056, 432, 14476, 22752, 15552, 18144, 19536], 'label': '31104.fx.36.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.p1', 'old_label': '36.ci1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ci1', 'subgroup_fusion': None, 'weyl_group': '864.3992'}
-
id: 186246392
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.u1', '216.x1', '324.s1', '324.cn1', '324.cs1'], 'contains': ['1296.bl1', '1296.cd1', '1296.co1', '1296.dw1', '1296.dy2', '1944.g1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [23401, 12384, 36, 15552, 18144], 'label': '31104.fx.648.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.w1', 'old_label': '648.u1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.u1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186246393
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.w1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.r1', '216.v1', '324.b1', '324.o1', '324.ct1'], 'contains': ['1296.cp1', '1296.dz1', '1296.eb1', '1296.gk1', '1296.jc1', '1944.f1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [21169, 1728, 36, 18144, 2592], 'label': '31104.fx.648.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '648.v1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.v1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
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id: 186246394
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.s1', '216.w1', '216.x1', '324.v1', '324.cp1', '324.ct1'], 'contains': ['1296.bm1', '1296.ce1', '1296.cp1', '1296.ea1', '1296.ec1', '1944.g1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [5689, 1728, 36, 2592, 15552], 'label': '31104.fx.648.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '648.w1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.w1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186246395
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.dg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.y1', '216.bb1', '324.c1', '324.g1', '324.w1'], 'contains': ['1296.cs1', '1296.cw1', '1296.da1', '1296.gl1', '1296.gs1', '1296.ht1', '1296.iv1', '1944.h1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [26485, 18576, 12138, 18648, 22752], 'label': '31104.fx.648.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.x1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.x1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
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id: 186246396
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ed1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.z1', '216.bf1', '324.d1', '324.h1', '324.w1'], 'contains': ['1296.cs1', '1296.cw1', '1296.dq1', '1296.gm1', '1296.hd1', '1296.hx1', '1296.jo1', '1944.j1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [29077, 18576, 12138, 18648, 22752], 'label': '31104.fx.648.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.y1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.y1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 186246397
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.dz1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.y1', '216.bg1', '324.a1', '324.e1', '324.x1'], 'contains': ['1296.ct1', '1296.cy1', '1296.dc1', '1296.gn1', '1296.gt1', '1296.ia1', '1296.iz1', '1944.h1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26485, 12096, 12138, 18648, 18576], 'label': '31104.fx.648.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '648.z1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.z1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 186246398
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ba1', '216.be1', '324.g1', '324.h1', '324.i1'], 'contains': ['1296.cs1', '1296.cx1', '1296.di1', '1296.go1', '1296.gx1', '1296.ie1', '1296.jg1', '1944.i1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [29503, 10368, 2628, 18648, 18576], 'label': '31104.fx.648.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.ba1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ba1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 186246399
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ba1', '216.bc1', '324.e1', '324.f1', '324.j1'], 'contains': ['1296.ct1', '1296.cy1', '1296.dk1', '1296.gp1', '1296.gy1', '1296.if1', '1296.ji1', '1944.i1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [26047, 12096, 2628, 18648, 18576], 'label': '31104.fx.648.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '648.bb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bb1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 186246400
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ba1', '216.bd1', '324.k1'], 'contains': ['1296.cu1', '1296.cz1', '1296.dm1', '1296.gq1', '1296.gz1', '1296.ig1', '1296.jj1', '1944.i1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [26047, 12096, 18612, 15552, 2592], 'label': '31104.fx.648.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.k1', 'old_label': '648.bc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bc1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186246401
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.eg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.z1', '216.bh1', '324.b1', '324.f1', '324.x1'], 'contains': ['1296.ct1', '1296.cy1', '1296.dz1', '1296.gr1', '1296.hf1', '1296.il1', '1296.js1', '1944.j1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [29077, 12096, 12138, 18648, 18576], 'label': '31104.fx.648.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '648.bd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bd1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 186246402
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ep1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.d1', '12.n1', '18.s1', '18.w1', '18.bm1'], 'contains': ['72.a1', '72.y1', '72.be1', '108.ei1', '108.eo1', '108.eu1'], 'core': '72.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [26047, 18576, 2592, 16056, 22752, 10368, 12096, 15552], 'label': '31104.fx.36.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '36.cj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cj1', 'subgroup_fusion': None, 'weyl_group': '864.4000'}
-
id: 186246403
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.dy1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.bi1', '324.a1', '324.f1', '324.bf1'], 'contains': ['1296.ct1', '1296.dn1', '1296.ha1', '1296.hg1', '1296.jk1', '1944.k1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [5713, 18576, 12138, 18648, 12096], 'label': '31104.fx.648.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '648.be1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.be1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 186246404
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.eo1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.bj1', '324.b1', '324.e1', '324.bf1'], 'contains': ['1296.ct1', '1296.eb1', '1296.he1', '1296.hh1', '1296.jt1', '1944.l1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [8305, 18576, 12138, 18648, 12096], 'label': '31104.fx.648.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '648.bf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bf1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
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id: 186246405
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.bc1', '216.bd1', '216.be1', '324.g1', '324.h1', '324.l1'], 'contains': ['1296.cv1', '1296.cw1', '1296.di1', '1296.hi1', '1296.hn1', '1296.hv1', '1296.jh1', '1944.i1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [19135, 22752, 2628, 18648, 18576], 'label': '31104.fx.648.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.bg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bg1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246406
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.dg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.bb1', '216.bg1', '324.c1', '324.g1', '324.bg1'], 'contains': ['1296.cv1', '1296.cx1', '1296.da1', '1296.hj1', '1296.hl1', '1296.hz1', '1296.iw1', '1944.h1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26485, 10368, 12138, 18648, 18576], 'label': '31104.fx.648.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '648.bh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bh1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246407
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ed1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.bf1', '216.bh1', '324.d1', '324.h1', '324.bg1'], 'contains': ['1296.cv1', '1296.cx1', '1296.dq1', '1296.hk1', '1296.hq1', '1296.ij1', '1296.jp1', '1944.j1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [29077, 10368, 12138, 18648, 18576], 'label': '31104.fx.648.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '648.bi1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bi1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246408
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.di1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.bi1', '216.bk1', '324.c1', '324.h1', '324.bk1'], 'contains': ['1296.cs1', '1296.cv1', '1296.do1', '1296.hb1', '1296.ho1', '1296.hr1', '1296.jm1', '1944.k1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 10368, 12138, 18648, 18576], 'label': '31104.fx.648.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '648.bj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bj1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 186246409
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.el1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.bj1', '216.bl1', '324.d1', '324.g1', '324.bk1'], 'contains': ['1296.cs1', '1296.cv1', '1296.ds1', '1296.hc1', '1296.hp1', '1296.hs1', '1296.jq1', '1944.l1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [8305, 10368, 12138, 18648, 18576], 'label': '31104.fx.648.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '648.bk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bk1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246410
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.bm1', '216.bo1', '324.c1', '324.h1', '324.bv1'], 'contains': ['1296.cw1', '1296.cx1', '1296.do1', '1296.hw1', '1296.ii1', '1296.in1', '1296.jn1', '1944.m1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 10368, 6, 18648, 18576], 'label': '31104.fx.648.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.bl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bl1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246411
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.u1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.bn1', '216.bp1', '324.d1', '324.g1', '324.bv1'], 'contains': ['1296.cw1', '1296.cx1', '1296.ds1', '1296.hy1', '1296.ik1', '1296.io1', '1296.jr1', '1944.n1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [8305, 10368, 6, 18648, 18576], 'label': '31104.fx.648.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.bm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bm1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246412
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.s1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.bo1', '324.a1', '324.f1', '324.bw1'], 'contains': ['1296.cy1', '1296.dn1', '1296.ih1', '1296.ip1', '1296.jl1', '1944.m1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [5713, 12096, 6, 18648, 18576], 'label': '31104.fx.648.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '648.bn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bn1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246413
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.d1', '12.o1', '18.n1', '18.x1', '18.bj1'], 'contains': ['72.b1', '108.ej1', '108.el1', '108.eo1', '108.ev1', '144.fh1'], 'core': '72.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [26047, 16056, 18576, 22752, 10368, 15552, 2592, 3100], 'label': '31104.fx.36.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '36.ck1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ck1', 'subgroup_fusion': None, 'weyl_group': '3456.di'}
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id: 186246414
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.w1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.bp1', '324.b1', '324.e1', '324.bw1'], 'contains': ['1296.cy1', '1296.eb1', '1296.im1', '1296.iq1', '1296.ju1', '1944.n1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [8305, 12096, 6, 18648, 18576], 'label': '31104.fx.648.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '648.bo1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bo1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246415
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.bq1', '216.bs1', '324.bx1', '324.cm1', '324.cu1'], 'contains': ['1296.bq1', '1296.bt1', '1296.da1', '1296.dd1', '1296.dt1', '1944.o1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [16057, 10368, 16092, 2592, 15552], 'label': '31104.fx.648.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.v1', 'old_label': '648.bp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bp1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246416
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.bq1', '216.bt1', '324.by1', '324.cn1', '324.cw1'], 'contains': ['1296.bs1', '1296.bv1', '1296.db1', '1296.de1', '1296.dy2', '1944.o1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [23401, 12384, 2700, 15552, 18144], 'label': '31104.fx.648.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.w1', 'old_label': '648.bq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bq1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246417
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.bq2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.bq1', '216.bt2', '324.by1', '324.co1', '324.cv1'], 'contains': ['1296.br1', '1296.bu1', '1296.db1', '1296.de2', '1296.dy1', '1944.o1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [5689, 12384, 16092, 18144, 15552], 'label': '31104.fx.648.bq2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.w1', 'old_label': '648.bq2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bq2', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246418
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.br1', '216.bu1', '324.g1', '324.m1', '324.cu1'], 'contains': ['1296.da1', '1296.di1', '1296.ds1', '1296.it1', '1296.it2', '1944.p1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [433, 10368, 468, 18144, 2592], 'label': '31104.fx.648.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '648.br1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.br1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186246419
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.br1', '216.bv1', '324.n1', '324.cv1', '324.cw1'], 'contains': ['1296.db1', '1296.dj1', '1296.dx1', '1296.iu1', '1944.p1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [8209, 12384, 18612, 15552, 2592], 'label': '31104.fx.648.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.w1', 'old_label': '648.bs1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bs1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246420
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.bs1', '216.bt1', '216.bt2', '324.cb1', '324.cp1', '324.cy1'], 'contains': ['1296.by1', '1296.bz1', '1296.dc1', '1296.df1', '1296.ec1', '1944.o1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [5689, 1728, 16092, 2592, 15552], 'label': '31104.fx.648.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '648.bt1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bt1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246421
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.bu1', '216.bv1', '324.e1', '324.o1', '324.cy1'], 'contains': ['1296.dc1', '1296.dk1', '1296.eb1', '1296.iy1', '1944.p1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [21169, 1728, 468, 18144, 2592], 'label': '31104.fx.648.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '648.bu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bu1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186246422
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.bw1', '216.bx1', '216.by1', '324.cd1', '324.cp1', '324.da1'], 'contains': ['1296.cf1', '1296.cj1', '1296.df1', '1296.dn1', '1296.ea1', '1944.q1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [20737, 1728, 16092, 2592, 15552], 'label': '31104.fx.648.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '648.bv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bv1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246423
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.bw1', '216.bz1', '324.ce1', '324.cm1', '324.db1'], 'contains': ['1296.cg1', '1296.ck1', '1296.dd1', '1296.do1', '1296.dr1', '1944.q1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1, 10368, 16092, 2592, 15552], 'label': '31104.fx.648.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.v1', 'old_label': '648.bw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bw1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 186246424
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.d1', '12.p1', '18.y1'], 'contains': ['72.cz1', '108.en1', '108.eo1', '108.ew1', '144.fi1'], 'core': '216.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [6, 16056, 432, 10368, 22752, 15552, 18144, 19536], 'label': '31104.fx.36.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1', 'old_label': '36.cl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cl1', 'subgroup_fusion': None, 'weyl_group': '1728.46101'}
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id: 186246425
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.bx1', '216.bz1', '324.cf1', '324.co1', '324.dc1'], 'contains': ['1296.ch1', '1296.cl1', '1296.de2', '1296.dp1', '1296.dv1', '1944.q1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [20737, 12384, 16092, 18144, 15552], 'label': '31104.fx.648.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.w1', 'old_label': '648.bx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bx1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246426
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.by1', '216.bz1', '324.cf1', '324.cn1', '324.dd1'], 'contains': ['1296.ci1', '1296.cm1', '1296.de1', '1296.dp1', '1296.dw1', '1944.q1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [20737, 12384, 2700, 15552, 18144], 'label': '31104.fx.648.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.w1', 'old_label': '648.by1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.by1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246427
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ca1', '216.cc1', '324.bx1', '324.cq1', '324.db1'], 'contains': ['1296.dd1', '1296.dq1', '1296.dt1', '1944.r1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [15625, 10368, 16092, 18144, 2592], 'label': '31104.fx.648.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.v1', 'old_label': '648.bz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bz1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246428
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.cb1', '216.cd1', '324.ce1', '324.cq1', '324.cu1'], 'contains': ['1296.dd1', '1296.dr1', '1296.ds1', '1944.s1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [433, 10368, 16092, 15552, 2592], 'label': '31104.fx.648.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.v1', 'old_label': '648.ca1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ca1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246429
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.cc1', '216.ce1', '324.by1', '324.cr1', '324.dd1'], 'contains': ['1296.de1', '1296.du1', '1296.dy1', '1944.r1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [5689, 12384, 2700, 18144, 15552], 'label': '31104.fx.648.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.w1', 'old_label': '648.cb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cb1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246430
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.cb2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.cc1', '216.ce2', '324.by1', '324.cs1', '324.dc1'], 'contains': ['1296.de2', '1296.du1', '1296.dy2', '1944.r1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [23401, 12384, 16092, 18144, 15552], 'label': '31104.fx.648.cb2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.w1', 'old_label': '648.cb2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cb2', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246431
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.cd1', '216.cf1', '324.cf1', '324.cr1', '324.cw1'], 'contains': ['1296.de1', '1296.dv1', '1296.dx1', '1944.s1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [8209, 12384, 2700, 2592, 15552], 'label': '31104.fx.648.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.w1', 'old_label': '648.cc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cc1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246432
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.cd1', '216.cg1', '324.cf1', '324.cs1', '324.cv1'], 'contains': ['1296.de2', '1296.dw1', '1296.dx1', '1944.s1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [8209, 12384, 16092, 2592, 15552], 'label': '31104.fx.648.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.w1', 'old_label': '648.cd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cd1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246433
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.ca1', '216.ce1', '216.ce2', '324.cb1', '324.ct1', '324.da1'], 'contains': ['1296.df1', '1296.dz1', '1296.ec1', '1944.r1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [5257, 1728, 16092, 18144, 2592], 'label': '31104.fx.648.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '648.ce1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ce1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246434
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.cb1', '216.cf1', '216.cg1', '324.cd1', '324.ct1', '324.cy1'], 'contains': ['1296.df1', '1296.ea1', '1296.eb1', '1944.s1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [21169, 1728, 16092, 15552, 2592], 'label': '31104.fx.648.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '648.cf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cf1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186247419
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.eq1', '576.y1', '576.bf1', '864.ib1'], 'contains': ['3456.s1', '5184.bb1', '5184.bf1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 576, 'diagramx': None, 'generators': [6, 18580, 28464], 'label': '31104.fx.1728.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.dw1', 'old_label': '1728.bw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.bw1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186246435
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1', '12.r1', '18.t1', '18.w1'], 'contains': ['72.a1', '72.z1', '72.bd1', '72.bx1', '72.cj1', '108.ex1', '108.ey1', '108.fe1'], 'core': '72.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [10405, 10368, 2592, 16056, 22752, 1728, 15552, 18576], 'label': '31104.fx.36.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '36.cm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cm1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186246436
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.ch1', '216.ci1', '324.f1', '324.o1', '324.da1'], 'contains': ['1296.dk1', '1296.dn1', '1296.dz1', '1296.jd1', '1944.t1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [20737, 1728, 468, 18144, 2592], 'label': '31104.fx.648.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '648.cg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cg1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186246437
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ch1', '216.cj1', '324.h1', '324.m1', '324.db1'], 'contains': ['1296.di1', '1296.do1', '1296.dq1', '1296.je1', '1296.je2', '1944.t1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1, 10368, 468, 18144, 2592], 'label': '31104.fx.648.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '648.ch1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ch1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186246438
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.ci1', '216.cj1', '324.n1', '324.dc1', '324.dd1'], 'contains': ['1296.dj1', '1296.dp1', '1296.du1', '1296.jf1', '1944.t1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [20737, 12384, 18612, 15552, 2592], 'label': '31104.fx.648.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.w1', 'old_label': '648.ci1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ci1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246439
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ck1', '216.cl1', '324.r1', '324.cu1', '324.db1'], 'contains': ['1296.di1', '1296.dr1', '1296.dt1', '1944.u1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [16057, 10368, 468, 15552, 2592], 'label': '31104.fx.648.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.v1', 'old_label': '648.cj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cj1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246440
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.cl1', '216.cm1', '324.s1', '324.cw1', '324.dc1'], 'contains': ['1296.dj1', '1296.dv1', '1296.dy2', '1944.u1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [23401, 12384, 18612, 18144, 15552], 'label': '31104.fx.648.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.w1', 'old_label': '648.ck1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ck1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246441
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.cl1', '216.cn1', '324.s1', '324.cv1', '324.dd1'], 'contains': ['1296.dj1', '1296.dw1', '1296.dy1', '1944.u1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [5689, 12384, 18612, 2592, 15552], 'label': '31104.fx.648.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.w1', 'old_label': '648.cl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cl1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246442
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.ck1', '216.cm1', '216.cn1', '324.v1', '324.cy1', '324.da1'], 'contains': ['1296.dk1', '1296.ea1', '1296.ec1', '1944.u1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [5689, 1728, 468, 15552, 2592], 'label': '31104.fx.648.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '648.cm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cm1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 186246443
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.co1', '216.cp1', '216.cq1', '324.i1', '324.l1', '324.m1', '324.p1', '324.q1', '324.r1', '324.dg1'], 'contains': ['1296.a1', '1296.l1', '1296.cn1', '1296.di1', '1296.ed1', '1296.jw1', '1296.jw2', '1296.lb1', '1296.lb2', '1944.v1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [36, 10368, 18576, 18144, 16056], 'label': '31104.fx.648.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '648.cn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cn1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246444
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.cq1', '216.cr1', '216.cs1', '324.n1', '324.s1', '324.dh1'], 'contains': ['1296.b1', '1296.c1', '1296.m1', '1296.n1', '1296.co1', '1296.dj1', '1296.ee1', '1296.jx1', '1296.lc1', '1944.v1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [36, 12384, 18576, 16056, 18144], 'label': '31104.fx.648.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.w1', 'old_label': '648.co1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.co1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186246445
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.cp1', '216.cr1', '324.j1', '324.o1', '324.t1', '324.v1', '324.di1'], 'contains': ['1296.e1', '1296.p2', '1296.cp1', '1296.dk1', '1296.ef1', '1296.jy1', '1296.ld2', '1944.v1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [36, 12096, 16056, 2592, 18576], 'label': '31104.fx.648.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '648.cp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cp1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246446
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': ['15552.e1', '15552.i1', '15552.d1', '15552.f1'], 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.b1', '4.c1', '6.a1', '6.c1', '6.e1', '32.b1'], 'core': '2.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [26047, 18576, 12096, 10368, 18144, 36, 3100, 16056, 22752, 15552, 5712], 'label': '31104.fx.2.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.b1', '4.c1', '6.a1'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '31104.fx', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1', 'subgroup_fusion': None, 'weyl_group': '31104.fx'}
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id: 186246447
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.b1', '3.b1'], 'contains': ['12.a1', '12.r1', '12.w1', '18.p1', '18.q1', '18.t1', '24.f1', '24.s1'], 'core': '12.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1, 2592, 22752, 10368, 15552, 36, 12096, 432, 16056, 5712], 'label': '31104.fx.6.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '6.g1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.g1', 'subgroup_fusion': None, 'weyl_group': '10368.je'}
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id: 186246448
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1', '12.s1', '12.t1', '18.o1'], 'contains': ['72.by1', '72.cl1', '72.cx1', '108.ex1', '108.ez1', '108.ff1', '108.fg1', '144.bs1'], 'core': '216.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [10405, 15552, 12940, 18576, 10368, 18144, 18216, 22752], 'label': '31104.fx.36.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '36.cn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cn1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
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id: 186246449
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.co1', '216.cp1', '216.cs1', '324.k1', '324.u1', '324.di1'], 'contains': ['1296.d1', '1296.g1', '1296.o1', '1296.r2', '1296.cr1', '1296.dm1', '1296.eg1', '1296.jy1', '1296.jz1', '1296.ld1', '1296.le2', '1944.v1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [36, 12096, 15552, 2592, 18576], 'label': '31104.fx.648.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.t1', 'old_label': '648.cq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cq1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186246450
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.co1', '216.cr1', '216.cs1', '324.di1'], 'contains': ['1296.e1', '1296.f1', '1296.g1', '1296.p1', '1296.q1', '1296.r1', '1296.cq1', '1296.dl1', '1296.eh1', '1296.jz1', '1296.le1', '1944.v1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [36, 12096, 15552, 16056, 15984], 'label': '31104.fx.648.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.di1', 'old_label': '648.cr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cr1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186246451
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.gc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ct1', '216.cw1', '324.i1', '324.w1', '324.y1', '324.bb1', '324.bc1', '324.bk1', '324.dj1'], 'contains': ['1296.cs1', '1296.ed1', '1296.ka1', '1296.kd1', '1296.lk1', '1944.w1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [17371, 18576, 16056, 2592, 10368], 'label': '31104.fx.648.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '648.cs1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cs1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
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id: 186246452
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.gc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ct1', '216.cv1', '324.j1', '324.x1', '324.z1', '324.bd1', '324.be1', '324.bf1', '324.dk1'], 'contains': ['1296.ct1', '1296.ef1', '1296.kb1', '1296.ke1', '1296.lo1', '1944.w1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [17371, 18576, 16056, 2592, 12096], 'label': '31104.fx.648.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '648.ct1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ct1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
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id: 186246453
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.gc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ct1', '216.cu1', '324.k1', '324.ba1', '324.dk1'], 'contains': ['1296.cu1', '1296.eg1', '1296.kc1', '1296.ke1', '1296.lp1', '1944.w1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [17371, 2592, 15552, 18576, 12096], 'label': '31104.fx.648.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.ba1', 'old_label': '648.cu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cu1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
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id: 186246454
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.gc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.cu1', '216.cv1', '216.cw1', '324.l1', '324.bg1', '324.bh1', '324.bi1', '324.bj1', '324.bk1', '324.dn1'], 'contains': ['1296.cv1', '1296.ed1', '1296.kh1', '1296.kj1', '1296.ll1', '1944.w1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [17371, 22752, 16056, 2592, 18576], 'label': '31104.fx.648.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '648.cv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cv1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186246455
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ep1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.cx1', '216.cy1', '216.cz1', '324.l1', '324.w1', '324.bl1', '324.bm1', '324.bn1', '324.bv1', '324.dp1'], 'contains': ['1296.cw1', '1296.ed1', '1296.kk1', '1296.kl1', '1296.lm1', '1944.x1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [6, 16056, 18576, 18144, 10368], 'label': '31104.fx.648.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '648.cw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cw1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
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id: 186246456
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ep1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.cz1', '216.da1', '324.i1', '324.bg1', '324.bo1', '324.br1', '324.bs1', '324.bv1', '324.ds1'], 'contains': ['1296.cx1', '1296.ed1', '1296.ko1', '1296.ku1', '1296.ln1', '1944.x1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [6, 22752, 18576, 18144, 16056], 'label': '31104.fx.648.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '648.cx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cx1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186246457
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ep1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.cy1', '216.da1', '324.j1', '324.x1', '324.bp1', '324.bt1', '324.bu1', '324.bw1', '324.dt1'], 'contains': ['1296.cy1', '1296.ef1', '1296.kp1', '1296.kv1', '1296.lq2', '1944.x1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [6, 12096, 16056, 2592, 18576], 'label': '31104.fx.648.cy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '648.cy1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cy1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186246458
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ep1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.cx1', '216.da1', '324.k1', '324.bq1', '324.dt1'], 'contains': ['1296.cz1', '1296.eg1', '1296.kq1', '1296.kv1', '1296.lq1', '1944.x1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26047, 12096, 15552, 18576, 2592], 'label': '31104.fx.648.cz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bb1', 'old_label': '648.cz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cz1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246459
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.r1', '12.t1', '12.u1', '18.p1', '18.x1', '18.ba1'], 'contains': ['72.b1', '108.ex1', '108.fa1', '108.fb1', '108.fh1', '144.bu1', '144.fn1'], 'core': '72.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [10405, 16056, 18576, 22752, 12460, 15552, 2592, 10368], 'label': '31104.fx.36.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.co1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.co1', 'subgroup_fusion': None, 'weyl_group': '384.17948'}
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id: 186246460
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.db1', '216.dc1', '324.m1', '324.w1', '324.bg1', '324.bx1', '324.bz1', '324.ca1', '324.dx1'], 'contains': ['1296.da1', '1296.dq1', '1296.ed1', '1296.kw1', '1296.kw2', '1944.y1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [10405, 2592, 18576, 18144, 22752], 'label': '31104.fx.648.da1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '648.da1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.da1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
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id: 186246461
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.db1', '216.dd1', '324.n1', '324.by1', '324.dy1'], 'contains': ['1296.db1', '1296.du1', '1296.ee1', '1296.kx1', '1944.y1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [10405, 2592, 18576, 15552, 12384], 'label': '31104.fx.648.db1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bd1', 'old_label': '648.db1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.db1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 186246462
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.dc1', '216.dd1', '324.o1', '324.x1', '324.cb1', '324.cc1', '324.dz1'], 'contains': ['1296.dc1', '1296.dz1', '1296.ef1', '1296.ky1', '1944.y1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [10405, 1728, 18576, 18144, 2592], 'label': '31104.fx.648.dc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '648.dc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dc1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186246463
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.de1', '216.df1', '216.dg1', '324.y1', '324.bh1', '324.bl1', '324.bo1', '324.bx1', '324.ce1', '324.dg1'], 'contains': ['1296.l1', '1296.s1', '1296.dd1', '1296.ed1', '1296.lb1', '1296.lb2', '1944.z1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [15588, 10368, 18576, 18144, 16056], 'label': '31104.fx.648.dd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '648.dd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dd1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246464
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.dg1', '216.dh1', '216.di1', '324.by1', '324.cf1', '324.dh1'], 'contains': ['1296.m1', '1296.n1', '1296.t1', '1296.u1', '1296.de1', '1296.de2', '1296.ee1', '1296.lc1', '1944.z1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [15588, 12384, 18576, 16056, 18144], 'label': '31104.fx.648.de1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.w1', 'old_label': '648.de1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.de1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186246465
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.df1', '216.dh1', '324.z1', '324.bp1', '324.cb1', '324.cd1', '324.di1'], 'contains': ['1296.p1', '1296.w1', '1296.df1', '1296.ef1', '1296.ld1', '1944.z1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [15588, 12096, 16056, 2592, 18576], 'label': '31104.fx.648.df1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '648.df1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.df1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246466
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.de1', '216.df1', '216.di1', '324.ba1', '324.bq1', '324.di1'], 'contains': ['1296.o1', '1296.r1', '1296.v1', '1296.y1', '1296.dh1', '1296.eg1', '1296.ld1', '1296.ld2', '1296.le1', '1944.z1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [108, 12096, 15552, 2592, 18576], 'label': '31104.fx.648.dg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.t1', 'old_label': '648.dg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dg1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186246467
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.de1', '216.dh1', '216.di1', '324.di1'], 'contains': ['1296.p2', '1296.q1', '1296.r2', '1296.w1', '1296.x1', '1296.y1', '1296.dg1', '1296.dg2', '1296.eh1', '1296.le1', '1296.le2', '1944.z1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [18612, 12096, 15552, 16056, 15984], 'label': '31104.fx.648.dh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.di1', 'old_label': '648.dh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dh1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186246468
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.dj1', '216.dk1', '324.o1', '324.bf1', '324.bw1', '324.cd1', '324.cg1', '324.ch1', '324.ee1'], 'contains': ['1296.dn1', '1296.eb1', '1296.ef1', '1296.lf1', '1944.ba1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1, 2592, 18576, 18144, 1728], 'label': '31104.fx.648.di1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '648.di1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.di1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
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id: 186246469
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.dj1', '216.dl1', '324.m1', '324.bk1', '324.bv1', '324.ce1', '324.ci1', '324.cj1', '324.ef1'], 'contains': ['1296.do1', '1296.ds1', '1296.ed1', '1296.lg1', '1296.lg2', '1944.ba1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1, 10368, 18576, 18144, 2592], 'label': '31104.fx.648.dj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '648.dj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dj1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186246470
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1', '12.s1', '12.u1'], 'contains': ['72.bz1', '72.cn1', '72.cy1', '108.ex1', '108.fc1', '108.fi1', '108.fi2', '144.bv1'], 'core': '216.b1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [10405, 2592, 29404, 18576, 10368, 15552, 3096, 22752], 'label': '31104.fx.36.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cp1', 'old_label': '36.cp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cp1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186246471
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.dk1', '216.dl1', '324.n1', '324.cf1', '324.eg1'], 'contains': ['1296.dp1', '1296.dx1', '1296.ee1', '1296.lh1', '1944.ba1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1, 12384, 18576, 15552, 2592], 'label': '31104.fx.648.dk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '648.dk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dk1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246472
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.gc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.dm1', '216.du1', '324.p1', '324.bj1', '324.bm1', '324.bo1', '324.bz1', '324.ci1', '324.dj1'], 'contains': ['1296.ed1', '1296.lk1', '1944.bb1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1819, 18576, 16056, 10368, 2592], 'label': '31104.fx.648.dl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '648.dl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dl1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
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id: 186246473
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.gc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.dn1', '216.do1', '216.du1', '324.q1', '324.bc1', '324.bl1', '324.br1', '324.ca1', '324.ci1', '324.dn1'], 'contains': ['1296.ed1', '1296.ll1', '1944.bb1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1819, 22752, 16056, 2592, 18576], 'label': '31104.fx.648.dm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '648.dm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dm1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186246474
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.dp1', '216.dv1', '324.r1', '324.bb1', '324.bi1', '324.bm1', '324.br1', '324.ce1', '324.dx1'], 'contains': ['1296.dr1', '1296.ed1', '1944.bc1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [26461, 2592, 18576, 10368, 15552], 'label': '31104.fx.648.dn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '648.dn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dn1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
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id: 186246475
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ep1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.dq1', '216.dr1', '216.dw1', '324.q1', '324.bb1', '324.bh1', '324.bs1', '324.bz1', '324.cj1', '324.dp1'], 'contains': ['1296.ed1', '1296.lm1', '1944.bd1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [10495, 18576, 16056, 22752, 2592], 'label': '31104.fx.648.do1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '648.do1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.do1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
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id: 186246476
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ep1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ds1', '216.dw1', '324.p1', '324.y1', '324.bi1', '324.bn1', '324.ca1', '324.cj1', '324.ds1'], 'contains': ['1296.ed1', '1296.ln1', '1944.bd1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [15558, 22752, 18144, 2664, 16056], 'label': '31104.fx.648.dp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '648.dp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dp1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186246477
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.dt1', '216.dx1', '324.r1', '324.bc1', '324.bj1', '324.bn1', '324.bs1', '324.bx1', '324.ef1'], 'contains': ['1296.dt1', '1296.ed1', '1944.be1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [16057, 10368, 18576, 15552, 2592], 'label': '31104.fx.648.dq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '648.dq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dq1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186246478
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.dv1', '216.dy1', '324.s1', '324.cf1', '324.dy1'], 'contains': ['1296.dv1', '1296.dw1', '1296.ee1', '1944.bc1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [26461, 15552, 18576, 12384, 2592], 'label': '31104.fx.648.dr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bd1', 'old_label': '648.dr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dr1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
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id: 186246479
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.dx1', '216.dz1', '324.s1', '324.by1', '324.eg1'], 'contains': ['1296.dy1', '1296.dy2', '1296.ee1', '1944.be1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [16057, 12384, 18576, 2592, 15552], 'label': '31104.fx.648.ds1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '648.ds1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ds1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246480
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.gc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.dm1', '216.do1', '324.t1', '324.be1', '324.bp1', '324.bt1', '324.cc1', '324.cg1', '324.dk1'], 'contains': ['1296.ef1', '1296.lp1', '1944.bb1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [27690, 18576, 2592, 12096, 2664], 'label': '31104.fx.648.dt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '648.dt1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dt1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
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id: 186246481
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.r1', '12.s1', '12.u1', '18.y1'], 'contains': ['72.cz1', '108.ex1', '108.fd1', '108.fd2', '108.fj1', '144.bx1', '144.fo1'], 'core': '216.b1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [10405, 16056, 432, 22752, 9168, 15552, 2592, 10368], 'label': '31104.fx.36.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.y1', 'old_label': '36.cq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cq1', 'subgroup_fusion': None, 'weyl_group': '192.955'}
-
id: 186246482
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.gc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.dm1', '216.dn1', '324.u1', '324.bq1', '324.dk1'], 'contains': ['1296.eg1', '1296.lo1', '1296.lp1', '1944.bb1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [17299, 18576, 15552, 12096, 2592], 'label': '31104.fx.648.du1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.ba1', 'old_label': '648.du1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.du1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
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id: 186246483
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.dv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.dp1', '216.dy1', '324.v1', '324.bd1', '324.bt1', '324.cd1', '324.dz1'], 'contains': ['1296.ea1', '1296.ef1', '1944.bc1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [26461, 1728, 18576, 15552, 2592], 'label': '31104.fx.648.dv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '648.dv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dv1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
-
id: 186246484
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ep1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.dr1', '216.ds1', '324.t1', '324.z1', '324.bd1', '324.bu1', '324.cc1', '324.ch1', '324.dt1'], 'contains': ['1296.ef1', '1296.lq1', '1944.bd1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [15558, 12096, 2592, 2664, 18576], 'label': '31104.fx.648.dw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '648.dw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dw1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
-
id: 186246485
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.dx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ep1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.dq1', '216.ds1', '324.u1', '324.ba1', '324.dt1'], 'contains': ['1296.eg1', '1296.lq1', '1296.lq2', '1944.bd1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [25975, 12096, 15552, 2592, 18576], 'label': '31104.fx.648.dx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bb1', 'old_label': '648.dx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dx1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246486
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.dt1', '216.dz1', '324.v1', '324.be1', '324.bu1', '324.cb1', '324.ee1'], 'contains': ['1296.ec1', '1296.ef1', '1944.be1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [16057, 2592, 18576, 1728, 15552], 'label': '31104.fx.648.dy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '648.dy1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dy1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
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id: 186246487
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.q1', '216.ea1', '216.eb1', '216.ef1', '216.eg1'], 'contains': ['1296.bd1', '1296.be1', '1296.bw1', '1296.ca1', '1296.ei1', '1296.et1', '1296.fi1', '1944.bf1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [20737, 12940, 36, 3096, 15552], 'label': '31104.fx.648.dz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.dz1', 'old_label': '648.dz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dz1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186246488
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.ea1', '216.ec1', '216.eh1', '216.ei1', '324.ck1'], 'contains': ['1296.ej1', '1296.eu1', '1296.fj1', '1944.bf1', '2592.ey1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [20737, 18144, 36, 12940, 72], 'label': '31104.fx.648.ea1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.ck1', 'old_label': '648.ea1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ea1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186246489
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.eb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['162.r1', '216.ea1', '216.ed1', '216.ee1', '216.ej1', '216.ek1'], 'contains': ['1296.ek1', '1296.ev1', '1296.fk1', '1944.bf1', '2592.ez1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [20737, 15552, 36, 16080, 18648], 'label': '31104.fx.648.eb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.eb1', 'old_label': '648.eb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.eb1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186246490
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.ec1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.eb1', '216.ec1', '216.ed1', '216.ee1', '216.el1', '216.em1', '324.cm1'], 'contains': ['1296.bf1', '1296.bj1', '1296.bq1', '1296.cg1', '1296.el1', '1296.ep1', '1296.ff1', '1944.bf1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [1, 10368, 36, 3096, 15552], 'label': '31104.fx.648.ec1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cm1', 'old_label': '648.ec1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ec1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246491
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.ed1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.eg1', '216.eh1', '216.ej1', '216.el1', '216.en1', '324.co1'], 'contains': ['1296.bg1', '1296.bk1', '1296.br1', '1296.ch1', '1296.em1', '1296.eq1', '1296.fg1', '1944.bf1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [20737, 12384, 36, 3096, 15552], 'label': '31104.fx.648.ed1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.co1', 'old_label': '648.ed1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ed1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246492
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.r1', '18.q1', '18.u1', '18.bb1'], 'contains': ['72.cr1', '108.ey1', '108.fb1', '108.fd1', '144.by1', '144.fp1'], 'core': '216.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [10405, 16056, 432, 16080, 10368, 15552, 2592, 1728], 'label': '31104.fx.36.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '36.cr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cr1', 'subgroup_fusion': None, 'weyl_group': '1152.155790'}
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id: 186246493
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.ee1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.ef1', '216.ei1', '216.ek1', '216.el1', '216.eo1', '324.cn1'], 'contains': ['1296.bh1', '1296.bl1', '1296.bs1', '1296.ci1', '1296.en1', '1296.er1', '1296.fh1', '1944.bf1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [20737, 12384, 36, 18216, 18144], 'label': '31104.fx.648.ee1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cn1', 'old_label': '648.ee1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ee1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246494
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.ef1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.em1', '216.en1', '216.eo1', '324.cp1'], 'contains': ['1296.bi1', '1296.bm1', '1296.by1', '1296.cf1', '1296.eo1', '1296.es1', '1296.fe1', '1944.bf1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [20737, 1728, 36, 3096, 15552], 'label': '31104.fx.648.ef1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cp1', 'old_label': '648.ef1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ef1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246495
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.eg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ep1', '216.eq1', '216.et1', '324.cm1'], 'contains': ['1296.bn1', '1296.bt1', '1296.cb1', '1296.ck1', '1296.ep1', '1296.fa1', '1296.ff1', '1944.bg1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [20737, 22752, 2628, 3096, 15552], 'label': '31104.fx.648.eg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cm1', 'old_label': '648.eg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.eg1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246496
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.eh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.ep1', '216.er1', '216.eu1', '324.co1'], 'contains': ['1296.bo1', '1296.bu1', '1296.cc1', '1296.cl1', '1296.eq1', '1296.fb1', '1296.fg1', '1944.bg1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [20737, 12384, 2628, 3096, 15552], 'label': '31104.fx.648.eh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.co1', 'old_label': '648.eh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.eh1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186246497
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.ei1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.ep1', '216.es1', '216.ev1', '324.cn1'], 'contains': ['1296.bp1', '1296.bv1', '1296.cd1', '1296.cm1', '1296.er1', '1296.fc1', '1296.fh1', '1944.bg1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [20737, 12384, 15588, 18216, 18144], 'label': '31104.fx.648.ei1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cn1', 'old_label': '648.ei1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ei1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186246498
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.eq1', '216.er1', '216.es1', '324.ck1'], 'contains': ['1296.eu1', '1296.ez1', '1296.fj1', '1944.bg1', '2592.ga1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [20737, 18144, 15588, 12940, 72], 'label': '31104.fx.648.ej1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.ck1', 'old_label': '648.ej1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ej1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 186246499
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.et1', '216.eu1', '216.ev1', '324.cp1'], 'contains': ['1296.bx1', '1296.bz1', '1296.ce1', '1296.cj1', '1296.es1', '1296.fd1', '1296.fe1', '1944.bg1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [20737, 1728, 2628, 3096, 15552], 'label': '31104.fx.648.ek1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cp1', 'old_label': '648.ek1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ek1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186246500
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.el1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.z1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.ew1', '216.ex1', '216.ey1', '324.ck1', '324.cl1', '324.de1'], 'contains': ['1296.ej1', '1296.ez1', '1296.ft1', '1944.bh1', '2592.h1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [36, 18144, 16056, 12940, 72], 'label': '31104.fx.648.el1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.q1', 'old_label': '648.el1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.el1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 186246501
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.em1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ew1', '216.ez1', '216.fa1', '324.cm1', '324.cq1', '324.dg1'], 'contains': ['1296.a1', '1296.s1', '1296.cn1', '1296.dd1', '1296.el1', '1296.fa1', '1296.fo1', '1944.bh1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [36, 10368, 18144, 3096, 15552], 'label': '31104.fx.648.em1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.u1', 'old_label': '648.em1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.em1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246502
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.en1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.ey1', '216.fa1', '216.fb1', '216.fc1', '324.cn1', '324.cr1', '324.dh1'], 'contains': ['1296.c1', '1296.u1', '1296.co1', '1296.de1', '1296.en1', '1296.fc1', '1296.fp1', '1944.bh1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [36, 12384, 3024, 18216, 18144], 'label': '31104.fx.648.en1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.y1', 'old_label': '648.en1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.en1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246503
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.t1', '18.i1', '18.v1', '18.bc1'], 'contains': ['72.cu1', '108.ez1', '108.fa1', '108.fb1', '108.fk1', '144.bz1'], 'core': '216.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [10405, 15624, 15984, 10368, 16080, 15552, 18144, 12460], 'label': '31104.fx.36.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '36.cs1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cs1', 'subgroup_fusion': None, 'weyl_group': '1152.157852'}
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id: 186246504
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.eo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.ex1', '216.fa1', '216.fd1', '324.co1', '324.cs1', '324.dh1'], 'contains': ['1296.b1', '1296.t1', '1296.co1', '1296.de2', '1296.em1', '1296.fb1', '1296.fq1', '1944.bh1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [36, 12384, 16056, 3096, 15552], 'label': '31104.fx.648.eo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '648.eo1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.eo1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246505
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.ep1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.ez1', '216.fb1', '216.fd1', '324.cp1', '324.ct1', '324.di1'], 'contains': ['1296.d1', '1296.f1', '1296.v1', '1296.x1', '1296.cp1', '1296.cq1', '1296.df1', '1296.dg1', '1296.eo1', '1296.fd1', '1296.fr1', '1944.bh1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [36, 12096, 18144, 18648, 18576], 'label': '31104.fx.648.ep1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '648.ep1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ep1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186246506
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.eq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.ez1', '216.fc1', '216.fd1', '324.di1'], 'contains': ['1296.e1', '1296.g1', '1296.w1', '1296.y1', '1296.cq1', '1296.cr1', '1296.dg2', '1296.dh1', '1296.eo1', '1296.fd2', '1296.fs1', '1944.bh1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [36, 12096, 18144, 16056, 2592], 'label': '31104.fx.648.eq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.di1', 'old_label': '648.eq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.eq1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186246507
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.er1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.fe1', '216.ff1', '216.fg1', '216.fh1', '324.cm1', '324.cu1', '324.dx1'], 'contains': ['1296.h1', '1296.da1', '1296.dr1', '1296.ep1', '1296.fo1', '1944.bi1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [10405, 15552, 16056, 2592, 10368], 'label': '31104.fx.648.er1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bd1', 'old_label': '648.er1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.er1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
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id: 186246508
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.es1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.fe1', '216.fi1', '216.fl1', '216.fm1', '324.cn1', '324.cv1', '324.dy1'], 'contains': ['1296.j1', '1296.db1', '1296.dw1', '1296.er1', '1296.fp1', '1944.bi1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [10405, 18144, 2664, 15552, 12384], 'label': '31104.fx.648.es1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bd1', 'old_label': '648.es1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.es1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
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id: 186246509
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.et1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.fe1', '216.fj1', '216.fk1', '216.fn1', '324.co1', '324.cw1', '324.dy1'], 'contains': ['1296.i1', '1296.db1', '1296.dv1', '1296.eq1', '1296.fq1', '1944.bi1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [10405, 15552, 16056, 18144, 12384], 'label': '31104.fx.648.et1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bd1', 'old_label': '648.et1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.et1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
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id: 186246510
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.eu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.ff1', '216.fi1', '216.fj1', '324.cp1', '324.cy1', '324.dz1'], 'contains': ['1296.k1', '1296.dc1', '1296.ea1', '1296.es1', '1296.fr1', '1944.bi1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [10405, 1728, 16056, 2592, 15552], 'label': '31104.fx.648.eu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '648.eu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.eu1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246511
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.ev1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.fg1', '216.fk1', '216.fl1', '324.ck1', '324.cx1', '324.ea1'], 'contains': ['1296.eu1', '1296.ft1', '1944.bi1', '2592.r1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [10405, 18144, 2664, 12940, 72], 'label': '31104.fx.648.ev1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '648.ev1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ev1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186246512
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.ew1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.fh1', '216.fm1', '216.fn1', '324.ec1'], 'contains': ['1296.ex1', '1296.fv1', '1944.bi1', '2592.s1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [10405, 15552, 16056, 29404, 3096], 'label': '31104.fx.648.ew1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cp1', 'old_label': '648.ew1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ew1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186246513
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.ex1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.z1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.fo1', '216.fp1', '216.fq1', '324.cx1', '324.cz1', '324.de1'], 'contains': ['1296.ez1', '1296.ft1', '1944.bj1', '2592.t1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [15588, 18144, 16056, 12940, 72], 'label': '31104.fx.648.ex1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.q1', 'old_label': '648.ex1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ex1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186246514
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.u1', '18.bd1'], 'contains': ['72.cv1', '108.fb1', '108.fc1', '108.fd2', '144.ca1'], 'core': '216.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [10405, 15624, 15984, 24268, 10368, 15552, 18144, 16080], 'label': '31104.fx.36.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1', 'old_label': '36.ct1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ct1', 'subgroup_fusion': None, 'weyl_group': '576.8654'}
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id: 186246515
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.ey1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.fo1', '216.fr1', '216.fs1', '324.cu1', '324.db1', '324.dg1'], 'contains': ['1296.l1', '1296.dd1', '1296.di1', '1296.fa1', '1296.fo1', '1944.bj1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [18612, 10368, 18144, 3096, 15552], 'label': '31104.fx.648.ey1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.u1', 'old_label': '648.ey1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ey1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246516
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.ez1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.fq1', '216.fs1', '216.ft1', '216.fu1', '324.cv1', '324.dc1', '324.dh1'], 'contains': ['1296.n1', '1296.de2', '1296.dj1', '1296.fc1', '1296.fp1', '1944.bj1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [15588, 12384, 3024, 18216, 18144], 'label': '31104.fx.648.ez1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.y1', 'old_label': '648.ez1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ez1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246517
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.fa1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.fp1', '216.fs1', '216.fv1', '324.cw1', '324.dd1', '324.dh1'], 'contains': ['1296.m1', '1296.de1', '1296.dj1', '1296.fb1', '1296.fq1', '1944.bj1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [16020, 12384, 16056, 3096, 15552], 'label': '31104.fx.648.fa1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '648.fa1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fa1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246518
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.fb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.fr1', '216.ft1', '216.fv1', '324.cy1', '324.da1', '324.di1'], 'contains': ['1296.o1', '1296.q1', '1296.df1', '1296.dg2', '1296.dk1', '1296.dl1', '1296.fd2', '1296.fr1', '1944.bj1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [2628, 12096, 18144, 18648, 18576], 'label': '31104.fx.648.fb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '648.fb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fb1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186246519
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.fc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.fr1', '216.fu1', '216.fv1', '324.di1'], 'contains': ['1296.p1', '1296.p2', '1296.r1', '1296.r2', '1296.dg1', '1296.dh1', '1296.dl1', '1296.dm1', '1296.fd1', '1296.fd2', '1296.fs1', '1944.bj1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [18612, 12096, 18144, 16056, 2592], 'label': '31104.fx.648.fc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.di1', 'old_label': '648.fc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fc1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 186246520
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.fd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.fw1', '216.fx1', '216.fy1', '324.cp1', '324.da1', '324.ee1'], 'contains': ['1296.z1', '1296.dn1', '1296.ec1', '1296.fe1', '1296.fr1', '1944.bk1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1, 15552, 16056, 2592, 1728], 'label': '31104.fx.648.fd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '648.fd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fd1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
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id: 186246521
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.fe1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.fw1', '216.fz1', '216.ga1', '324.cm1', '324.db1', '324.ef1'], 'contains': ['1296.ba1', '1296.do1', '1296.dt1', '1296.ff1', '1296.fo1', '1944.bk1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1, 10368, 16056, 2592, 15552], 'label': '31104.fx.648.fe1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.be1', 'old_label': '648.fe1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fe1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246522
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.ff1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.fx1', '216.ga1', '216.gc1', '216.gd1', '324.cn1', '324.dc1', '324.eg1'], 'contains': ['1296.bc1', '1296.dp1', '1296.dy2', '1296.fh1', '1296.fp1', '1944.bk1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1, 12384, 2664, 15552, 18144], 'label': '31104.fx.648.ff1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '648.ff1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ff1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246523
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.fg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.fy1', '216.ga1', '216.gb1', '324.co1', '324.dd1', '324.eg1'], 'contains': ['1296.bb1', '1296.dp1', '1296.dy1', '1296.fg1', '1296.fq1', '1944.bk1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1, 12384, 16056, 18144, 15552], 'label': '31104.fx.648.fg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '648.fg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fg1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246524
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.fh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.fz1', '216.gb1', '216.gc1', '324.ck1', '324.cz1', '324.eh1'], 'contains': ['1296.fj1', '1296.ft1', '1944.bk1', '2592.bn1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1, 18144, 15552, 556, 72], 'label': '31104.fx.648.fh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.q1', 'old_label': '648.fh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fh1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186246525
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1', '18.r1'], 'contains': ['72.ca1', '72.co1', '72.da1', '108.fe1', '108.fg1', '108.fi1', '144.cb1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [10405, 1728, 12384, 18576, 12940, 18144, 18216, 15552], 'label': '31104.fx.36.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '36.cu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cu1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
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id: 186246526
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.fi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.fz1', '216.gb1', '216.gd1', '324.ej1'], 'contains': ['1296.fm1', '1296.fu1', '1944.bk1', '2592.bo1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1, 18144, 15552, 10924, 72], 'label': '31104.fx.648.fi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.ej1', 'old_label': '648.fi1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fi1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186246527
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.fj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ge1', '216.gg1', '216.gi1', '216.gj1', '324.cq1', '324.db1', '324.dx1'], 'contains': ['1296.dq1', '1296.dr1', '1296.fo1', '1944.bl1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [10837, 2592, 16056, 10368, 15552], 'label': '31104.fx.648.fj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bd1', 'old_label': '648.fj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fj1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
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id: 186246528
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.fk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.gf1', '216.gh1', '216.gk1', '324.cq1', '324.cu1', '324.ef1'], 'contains': ['1296.ds1', '1296.dt1', '1296.fo1', '1944.bm1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [433, 10368, 16056, 15552, 2592], 'label': '31104.fx.648.fk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.be1', 'old_label': '648.fk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fk1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246529
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.fl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.gj1', '216.gl1', '216.gr1', '216.gu1', '324.cr1', '324.dc1', '324.dy1'], 'contains': ['1296.du1', '1296.dv1', '1296.fp1', '1944.bl1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [28981, 15552, 2664, 12384, 2592], 'label': '31104.fx.648.fl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bd1', 'old_label': '648.fl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fl1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
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id: 186246530
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.fm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.gj1', '216.gm1', '216.gp1', '216.gv1', '324.cs1', '324.dd1', '324.dy1'], 'contains': ['1296.du1', '1296.dw1', '1296.fq1', '1944.bl1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [28981, 15552, 16056, 12384, 2592], 'label': '31104.fx.648.fm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bd1', 'old_label': '648.fm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fm1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
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id: 186246531
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.fn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.gk1', '216.gn1', '216.gs1', '216.gt1', '324.cr1', '324.cv1', '324.eg1'], 'contains': ['1296.dx1', '1296.dy1', '1296.fp1', '1944.bm1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [18577, 12384, 2664, 2592, 15552], 'label': '31104.fx.648.fn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '648.fn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fn1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246532
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.fo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.gk1', '216.go1', '216.gq1', '324.cs1', '324.cw1', '324.eg1'], 'contains': ['1296.dx1', '1296.dy2', '1296.fq1', '1944.bm1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [18577, 12384, 16056, 2592, 15552], 'label': '31104.fx.648.fo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '648.fo1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fo1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246533
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.fp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.ge1', '216.gl1', '216.gm1', '324.ct1', '324.da1', '324.dz1'], 'contains': ['1296.dz1', '1296.ea1', '1296.fr1', '1944.bl1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [10837, 1728, 16056, 15552, 2592], 'label': '31104.fx.648.fp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '648.fp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fp1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246534
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.fq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.gf1', '216.gn1', '216.go1', '324.ct1', '324.cy1', '324.ee1'], 'contains': ['1296.eb1', '1296.ec1', '1296.fr1', '1944.bm1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [433, 2592, 16056, 1728, 15552], 'label': '31104.fx.648.fq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '648.fq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fq1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
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id: 186246535
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.fr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.gg1', '216.gp1', '216.gr1', '324.cl1', '324.cz1', '324.ea1'], 'contains': ['1296.ft1', '1944.bl1', '2592.bx1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [28981, 18144, 2592, 31084, 18216], 'label': '31104.fx.648.fr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '648.fr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fr1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186246536
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.s1'], 'contains': ['72.dd1', '108.fg1', '108.fi2', '108.fj1', '144.cd1', '144.cf1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [10405, 15624, 15984, 24268, 12384, 15552, 18144, 9168], 'label': '31104.fx.36.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1', 'old_label': '36.cv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cv1', 'subgroup_fusion': None, 'weyl_group': '288.1026'}
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id: 186246537
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.fs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.gh1', '216.gq1', '216.gs1', '324.cl1', '324.cx1', '324.eh1'], 'contains': ['1296.ft1', '1944.bm1', '2592.by1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [18577, 18144, 2592, 18700, 18216], 'label': '31104.fx.648.fs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.q1', 'old_label': '648.fs1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fs1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186246538
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.ft1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.gh1', '216.gq1', '216.gt1', '324.ej1'], 'contains': ['1296.fu1', '1944.bm1', '2592.bz1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [18577, 18144, 2592, 29068, 18216], 'label': '31104.fx.648.ft1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.ej1', 'old_label': '648.ft1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ft1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186246539
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.fu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.gi1', '216.gu1', '216.gv1', '324.ec1'], 'contains': ['1296.fv1', '1944.bl1', '2592.ca1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [28981, 15552, 2592, 27316, 18648], 'label': '31104.fx.648.fu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cp1', 'old_label': '648.fu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fu1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186246540
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.fv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.b1', '216.hc1', '216.hd1', '216.he1', '216.hf1', '216.hg1', '216.hh1', '216.hh2', '216.hi1', '324.dh1', '324.dy1', '324.eg1'], 'contains': ['1296.ee1', '1296.fp1', '1296.fq1', '1944.a1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [16056, 12384, 18576, 18144, 15552], 'label': '31104.fx.648.fv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '648.fv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fv1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
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id: 186246541
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.fw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.gw1', '216.hc1', '324.di1', '324.dk1', '324.dt1', '324.dz1', '324.ee1'], 'contains': ['1296.ef1', '1296.eg1', '1296.eh1', '1296.fr1', '1296.fs1', '1944.a1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [16056, 12096, 18576, 18144, 15552], 'label': '31104.fx.648.fw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '648.fw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fw1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186246542
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.fx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.fc1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.gx1', '216.hd1', '216.he1', '216.hj1', '216.hk1', '216.hl1', '216.hm1', '324.de1', '324.ea1', '324.eh1'], 'contains': ['1296.ft1', '1944.a1', '2592.ck1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [18576, 18144, 15552, 24460, 72], 'label': '31104.fx.648.fx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '648.fx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fx1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
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id: 186246543
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.fy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.ba1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.a1', '216.gy1', '216.hf1', '216.hj1', '216.hl1', '216.hn1', '216.ho1', '324.df1', '324.dl1', '324.do1', '324.dq1', '324.du1', '324.eb1', '324.ei1'], 'contains': ['1944.a1', '2592.cm1', '2592.et1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [5712, 15552, 15624, 432, 2592], 'label': '31104.fx.648.fy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '648.fy1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fy1', 'subgroup_fusion': None, 'weyl_group': '576.8654'}
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id: 186246544
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.fz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.df1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.gx1', '216.hd1', '216.hg1', '216.hj1', '216.hk1', '216.hn1', '216.ho1', '216.hp1', '216.hp2', '324.ej1'], 'contains': ['1296.fu1', '1944.a1', '2592.cn1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [18576, 18144, 15552, 10924, 72], 'label': '31104.fx.648.fz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '648.fz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fz1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
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id: 186246545
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.ga1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.gy1', '216.gz1', '216.hf1', '216.hj1', '216.hk1', '216.hm1', '216.hn1', '216.hp1', '216.hp2', '324.dr1', '324.dv1', '324.ek1'], 'contains': ['1944.a1', '2592.cp1', '2592.eu1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [28464, 15552, 15624, 432, 2592], 'label': '31104.fx.648.ga1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.m1', 'old_label': '648.ga1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ga1', 'subgroup_fusion': None, 'weyl_group': '576.8654'}
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id: 186246546
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.gb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.df1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.ha1', '216.hh1', '216.hh2', '324.ec1'], 'contains': ['1296.fv1', '1296.fw1', '1944.a1', '2592.cq1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [18576, 15552, 18144, 11764, 18648], 'label': '31104.fx.648.gb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cp1', 'old_label': '648.gb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gb1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186246547
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.t1', '18.j1'], 'contains': ['72.de1', '108.ff1', '108.fg1', '108.fh1', '108.fk1', '144.ce1', '144.cg1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [10405, 15624, 15984, 12384, 16080, 15552, 18144, 12460], 'label': '31104.fx.36.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '36.cw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cw1', 'subgroup_fusion': None, 'weyl_group': '576.8657'}
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id: 186246548
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.gc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.hb1', '216.hb2', '216.hi1', '324.dm1', '324.dw1', '324.ed1'], 'contains': ['1944.a1', '2592.cs1', '2592.ev1', '2592.ev2'], 'core': '1944.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [29904, 15552, 15624, 432, 2592], 'label': '31104.fx.648.gc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.y1', 'old_label': '648.gc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gc1', 'subgroup_fusion': None, 'weyl_group': '192.955'}
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id: 186246549
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.gd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bl1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.hq1', '216.hs1', '324.c1', '324.em1', '324.eq1'], 'contains': ['1296.fx1', '1296.gb1', '1296.gf1', '1296.gs1', '1296.hb1', '1296.hz1', '1296.ii1', '1944.bn1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 22752, 21678, 36, 18576], 'label': '31104.fx.648.gd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.gd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gd1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246550
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.ge1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bo1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.hq1', '216.ht1', '324.a1', '324.en1', '324.ep1'], 'contains': ['1296.fy1', '1296.gd1', '1296.gi1', '1296.gt1', '1296.ha1', '1296.ia1', '1296.ih1', '1944.bn1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 12096, 2670, 36, 18576], 'label': '31104.fx.648.ge1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '648.ge1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ge1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246551
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.gf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bq1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.hr1', '216.hv1', '324.d1', '324.em1', '324.eq1'], 'contains': ['1296.fx1', '1296.gf1', '1296.gg1', '1296.hc1', '1296.hd1', '1296.ij1', '1296.ik1', '1944.bo1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [8305, 22752, 21678, 36, 18576], 'label': '31104.fx.648.gf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.gf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gf1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246552
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.gg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bp1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.hr1', '216.hu1', '324.b1', '324.en1', '324.ep1'], 'contains': ['1296.fy1', '1296.gi1', '1296.gk1', '1296.he1', '1296.hf1', '1296.il1', '1296.im1', '1944.bo1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [8305, 12096, 2598, 36, 18576], 'label': '31104.fx.648.gg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '648.gg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gg1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246553
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.gh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.hw1', '324.a1', '324.ep1'], 'contains': ['1296.fy1', '1296.gd1', '1296.gn1', '1296.hg1', '1296.ip1', '1296.ls1', '1296.lu1', '1944.bp1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [5713, 12096, 6, 36, 18576], 'label': '31104.fx.648.gh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '648.gh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gh1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246554
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.gi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.hx1', '324.b1', '324.ep1'], 'contains': ['1296.fy1', '1296.gk1', '1296.gr1', '1296.hh1', '1296.iq1', '1944.bq1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [8305, 12096, 6, 36, 18576], 'label': '31104.fx.648.gi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '648.gi1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gi1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246555
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.gj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bt1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.hs1', '216.ht1', '324.c1', '324.eo1', '324.er1'], 'contains': ['1296.ga1', '1296.gb1', '1296.ge1', '1296.hl1', '1296.ho1', '1296.ht1', '1296.hw1', '1944.bn1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 22752, 21606, 36, 18576], 'label': '31104.fx.648.gj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.gj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gj1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246556
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.gk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bx1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.hu1', '216.hv1', '324.d1', '324.eo1', '324.er1'], 'contains': ['1296.ga1', '1296.ge1', '1296.gg1', '1296.hp1', '1296.hq1', '1296.hx1', '1296.hy1', '1944.bo1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [8305, 22752, 21606, 36, 18576], 'label': '31104.fx.648.gk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.gk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gk1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246557
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.gl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bi1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.hw1', '216.hy1', '324.c1', '324.eq1', '324.er1'], 'contains': ['1296.fx1', '1296.ga1', '1296.gb1', '1296.gl1', '1296.hj1', '1296.hr1', '1296.in1', '1296.lt1', '1296.lv1', '1944.bp1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 10368, 24198, 36, 18576], 'label': '31104.fx.648.gl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.gl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gl1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246558
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '6.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.c1', '3.b1'], 'contains': ['12.d1', '12.l1', '12.r1', '18.u1', '18.w1', '18.x1', '18.y1', '24.t1'], 'core': '12.d1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [26485, 2592, 10368, 22752, 15552, 12138, 12096, 18576, 2664, 28012], 'label': '31104.fx.6.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '6.h1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.h1', 'subgroup_fusion': None, 'weyl_group': '3456.de'}
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id: 186246559
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.w1', '18.q1', '18.be1', '18.bk1'], 'contains': ['72.cr1', '108.fl1', '108.fp1', '144.ck1', '144.fr1'], 'core': '216.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1, 16056, 432, 12096, 10368, 15552, 2592, 5712], 'label': '31104.fx.36.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.cx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cx1', 'subgroup_fusion': None, 'weyl_group': '3456.gu'}
-
id: 186246560
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.gm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bk1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.hx1', '216.hz1', '324.d1', '324.eq1', '324.er1'], 'contains': ['1296.fx1', '1296.ga1', '1296.gg1', '1296.gm1', '1296.hk1', '1296.hs1', '1296.io1', '1944.bq1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [8305, 10368, 24198, 36, 18576], 'label': '31104.fx.648.gm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.gm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gm1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186246561
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.gn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ia1', '216.ib1', '324.c1', '324.em1', '324.eo1'], 'contains': ['1296.gb1', '1296.ge1', '1296.gf1', '1296.iv1', '1296.iw1', '1296.jm1', '1296.jn1', '1944.br1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 22752, 24270, 36, 18576], 'label': '31104.fx.648.gn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.gn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gn1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186246562
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.go1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.ch1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.ib1', '324.a1', '324.en1'], 'contains': ['1296.gd1', '1296.gi1', '1296.iz1', '1296.jk1', '1296.jl1', '1944.br1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [5713, 12096, 78, 36, 18576], 'label': '31104.fx.648.go1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '648.go1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.go1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186246563
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.gp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cj1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ic1', '216.id1', '324.d1', '324.em1', '324.eo1'], 'contains': ['1296.ge1', '1296.gf1', '1296.gg1', '1296.jo1', '1296.jp1', '1296.jq1', '1296.jr1', '1944.bs1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [8305, 22752, 24270, 36, 18576], 'label': '31104.fx.648.gp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.gp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gp1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186246564
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.gq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.ck1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.ic1', '324.b1', '324.en1'], 'contains': ['1296.gi1', '1296.gk1', '1296.js1', '1296.jt1', '1296.ju1', '1944.bs1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [8305, 12096, 78, 36, 18576], 'label': '31104.fx.648.gq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '648.gq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gq1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186246565
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.gr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ie1', '216.ik1', '324.c1', '324.es1', '324.ew1'], 'contains': ['1296.gl1', '1296.gu1', '1296.hb1', '1296.hu1', '1296.hw1', '1296.ir1', '1296.iw1', '1944.bt1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 10368, 21678, 108, 18576], 'label': '31104.fx.648.gr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.gr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gr1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 186246566
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.gs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.u1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.if1', '216.il1', '324.d1', '324.es1', '324.ew1'], 'contains': ['1296.gm1', '1296.gu1', '1296.hc1', '1296.hu1', '1296.hy1', '1296.ja1', '1296.jp1', '1944.bu1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [8305, 22752, 21606, 108, 18576], 'label': '31104.fx.648.gs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.gs1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gs1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 186246567
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.gt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ie1', '216.io1', '324.a1', '324.et1', '324.eu1'], 'contains': ['1296.gn1', '1296.gv1', '1296.ha1', '1296.ic1', '1296.ih1', '1296.ix1', '1296.iz1', '1944.bt1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 12096, 2598, 108, 18576], 'label': '31104.fx.648.gt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '648.gt1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gt1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 186246568
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.gu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.w1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.if1', '216.ip1', '324.b1', '324.et1', '324.eu1'], 'contains': ['1296.gr1', '1296.gv1', '1296.he1', '1296.ic1', '1296.im1', '1296.jc1', '1296.js1', '1944.bu1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [8305, 12096, 2598, 108, 18576], 'label': '31104.fx.648.gu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '648.gu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gu1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 186246569
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.gv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ig1', '216.im1', '324.g1', '324.eq1', '324.es1'], 'contains': ['1296.gl1', '1296.go1', '1296.hc1', '1296.hv1', '1296.hz1', '1296.io1', '1296.it1', '1944.bv1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [8305, 22752, 24198, 2700, 18576], 'label': '31104.fx.648.gv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.gv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gv1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 186246570
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.w1', '18.bl1'], 'contains': ['72.cs1', '108.fl1', '108.fq1', '144.cl1', '144.fs1'], 'core': '648.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1, 16056, 18576, 1728, 22752, 15552, 2592, 76], 'label': '31104.fx.36.cy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bl1', 'old_label': '36.cy1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cy1', 'subgroup_fusion': None, 'weyl_group': '1728.12469'}
-
id: 186246571
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.gw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ih1', '216.in1', '324.h1', '324.eq1', '324.es1'], 'contains': ['1296.gm1', '1296.go1', '1296.hb1', '1296.hv1', '1296.ij1', '1296.in1', '1296.je1', '1944.bw1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 22752, 24198, 2700, 18576], 'label': '31104.fx.648.gw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.gw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gw1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 186246572
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.gx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ig1', '216.iq1', '324.e1', '324.ep1', '324.et1'], 'contains': ['1296.gn1', '1296.gp1', '1296.he1', '1296.ia1', '1296.if1', '1296.iq1', '1296.iy1', '1944.bv1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [8305, 12096, 6, 2628, 18576], 'label': '31104.fx.648.gx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '648.gx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gx1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 186246573
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.gy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ih1', '216.ir1', '324.f1', '324.ep1', '324.et1'], 'contains': ['1296.gp1', '1296.gr1', '1296.ha1', '1296.if1', '1296.il1', '1296.ip1', '1296.jd1', '1944.bw1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 12096, 6, 2628, 18576], 'label': '31104.fx.648.gy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '648.gy1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gy1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 186246574
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.gz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.v1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ii1', '216.is1', '324.g1', '324.em1', '324.ew1'], 'contains': ['1296.gs1', '1296.gx1', '1296.hc1', '1296.it2', '1296.iw1', '1296.jh1', '1296.jr1', '1944.bx1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [8305, 22752, 24270, 2628, 18576], 'label': '31104.fx.648.gz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.gz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gz1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 186246575
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.ha1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ii1', '216.it1', '324.e1', '324.en1', '324.eu1'], 'contains': ['1296.gt1', '1296.gy1', '1296.he1', '1296.iy1', '1296.iz1', '1296.ji1', '1296.ju1', '1944.bx1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [8305, 12096, 78, 2628, 18576], 'label': '31104.fx.648.ha1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '648.ha1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ha1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 186246576
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.hb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ij1', '216.iu1', '324.f1', '324.en1', '324.eu1'], 'contains': ['1296.gy1', '1296.ha1', '1296.hf1', '1296.jd1', '1296.ji1', '1296.jl1', '1296.js1', '1944.by1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 12096, 78, 2628, 18576], 'label': '31104.fx.648.hb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '648.hb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.hb1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 186246577
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.hc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.v1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ij1', '216.iv1', '324.h1', '324.em1', '324.ew1'], 'contains': ['1296.gx1', '1296.hb1', '1296.hd1', '1296.je2', '1296.jh1', '1296.jn1', '1296.jp1', '1944.by1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 22752, 24270, 2628, 18576], 'label': '31104.fx.648.hc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.hc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.hc1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 186246578
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.hd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.iw1', '216.iy1', '324.e1', '324.ep1', '324.eu1'], 'contains': ['1296.gn1', '1296.gp1', '1296.gt1', '1296.gy1', '1296.hh1', '1296.im1', '1296.iy1', '1944.bz1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [8305, 12096, 2598, 2628, 18576], 'label': '31104.fx.648.hd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '648.hd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.hd1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 186246579
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.he1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ix1', '216.iz1', '324.f1', '324.ep1', '324.eu1'], 'contains': ['1296.gp1', '1296.gr1', '1296.gy1', '1296.hf1', '1296.hg1', '1296.ih1', '1296.jd1', '1944.ca1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 12096, 2598, 2628, 18576], 'label': '31104.fx.648.he1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '648.he1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.he1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246580
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.hf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.s1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.ja1', '324.a1', '324.eu1'], 'contains': ['1296.gt1', '1296.gv1', '1296.hg1', '1296.ix1', '1296.jl1', '1944.cb1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [5713, 12096, 78, 108, 18576], 'label': '31104.fx.648.hf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '648.hf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.hf1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246581
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.v1', '12.w1', '18.t1', '18.z1', '18.bm1'], 'contains': ['72.a1', '72.bb1', '72.bf1', '72.cf1', '72.ck1', '108.fl1', '108.fm1', '108.fr1'], 'core': '72.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1, 2592, 15552, 16056, 12096, 10368, 22752, 18576], 'label': '31104.fx.36.cz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '36.cz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cz1', 'subgroup_fusion': None, 'weyl_group': '288.977'}
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id: 186246582
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.hg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.w1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.jb1', '324.b1', '324.eu1'], 'contains': ['1296.gv1', '1296.hf1', '1296.hh1', '1296.jc1', '1296.ju1', '1944.cc1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [8305, 12096, 78, 108, 18576], 'label': '31104.fx.648.hg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '648.hg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.hg1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246583
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.hh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ik1', '216.io1', '324.c1', '324.ev1', '324.ex1'], 'contains': ['1296.hj1', '1296.hm1', '1296.ho1', '1296.ib1', '1296.ii1', '1296.ir1', '1296.iv1', '1944.bt1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 22752, 21678, 108, 18576], 'label': '31104.fx.648.hh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.hh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.hh1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246584
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.hi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.u1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.il1', '216.ip1', '324.d1', '324.ev1', '324.ex1'], 'contains': ['1296.hk1', '1296.hm1', '1296.hp1', '1296.ib1', '1296.ik1', '1296.ja1', '1296.jo1', '1944.bu1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [8305, 22752, 21678, 108, 18576], 'label': '31104.fx.648.hi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.hi1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.hi1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246585
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.hj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.n1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.im1', '216.iq1', '324.g1', '324.er1', '324.ev1'], 'contains': ['1296.hi1', '1296.hj1', '1296.hp1', '1296.ht1', '1296.ie1', '1296.io1', '1296.it2', '1944.bv1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [8305, 22752, 24198, 2628, 18576], 'label': '31104.fx.648.hj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.hj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.hj1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246586
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.hk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.n1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.in1', '216.ir1', '324.h1', '324.er1', '324.ev1'], 'contains': ['1296.hi1', '1296.hk1', '1296.ho1', '1296.hx1', '1296.ie1', '1296.in1', '1296.je2', '1944.bw1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 22752, 24198, 2628, 18576], 'label': '31104.fx.648.hk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.hk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.hk1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246587
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.hl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.is1', '216.it1', '324.g1', '324.eo1', '324.ex1'], 'contains': ['1296.hl1', '1296.hn1', '1296.hp1', '1296.it1', '1296.iv1', '1296.jg1', '1296.jr1', '1944.bx1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [8305, 22752, 24270, 2700, 18576], 'label': '31104.fx.648.hl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.hl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.hl1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246588
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.hm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.iu1', '216.iv1', '324.h1', '324.eo1', '324.ex1'], 'contains': ['1296.hn1', '1296.ho1', '1296.hq1', '1296.je1', '1296.jg1', '1296.jn1', '1296.jo1', '1944.by1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 22752, 24270, 2700, 18576], 'label': '31104.fx.648.hm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.hm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.hm1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246589
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.hn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.n1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.iw1', '216.jc1', '324.g1', '324.er1', '324.ew1'], 'contains': ['1296.gl1', '1296.gx1', '1296.hi1', '1296.hl1', '1296.hs1', '1296.hy1', '1296.it2', '1944.bz1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [8305, 22752, 21606, 2628, 18576], 'label': '31104.fx.648.hn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.hn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.hn1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246590
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.ho1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.n1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ix1', '216.jd1', '324.h1', '324.er1', '324.ew1'], 'contains': ['1296.gm1', '1296.gx1', '1296.hi1', '1296.hq1', '1296.hr1', '1296.hw1', '1296.je2', '1944.ca1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 10368, 21678, 2700, 18576], 'label': '31104.fx.648.ho1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.ho1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ho1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246591
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.hp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.iy1', '216.jc1', '324.g1', '324.eq1', '324.ex1'], 'contains': ['1296.go1', '1296.gs1', '1296.hj1', '1296.hn1', '1296.hs1', '1296.ik1', '1296.it1', '1944.bz1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [8305, 22752, 21678, 2700, 18576], 'label': '31104.fx.648.hp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.hp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.hp1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246592
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.v1', '18.r1'], 'contains': ['72.cg1', '72.cp1', '72.da1', '108.fm1', '108.ft1', '144.cn1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1, 556, 12384, 18576, 15552, 18144, 18216, 1728], 'label': '31104.fx.36.da1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.r1', 'old_label': '36.da1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.da1', 'subgroup_fusion': None, 'weyl_group': '864.4000'}
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id: 186246593
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.hq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.iz1', '216.jd1', '324.h1', '324.eq1', '324.ex1'], 'contains': ['1296.go1', '1296.hd1', '1296.hk1', '1296.hn1', '1296.hr1', '1296.ii1', '1296.je1', '1944.ca1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 22752, 21678, 2700, 18576], 'label': '31104.fx.648.hq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.hq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.hq1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246594
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.hr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ja1', '216.je1', '324.c1', '324.ew1', '324.ex1'], 'contains': ['1296.gs1', '1296.gu1', '1296.hl1', '1296.hm1', '1296.hr1', '1296.ir1', '1296.jn1', '1944.cb1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 22752, 24270, 108, 18576], 'label': '31104.fx.648.hr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.hr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.hr1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246595
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.hs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.u1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.jb1', '216.jf1', '324.d1', '324.ew1', '324.ex1'], 'contains': ['1296.gu1', '1296.hd1', '1296.hm1', '1296.hq1', '1296.hs1', '1296.ja1', '1296.jr1', '1944.cc1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [8305, 22752, 24270, 108, 18576], 'label': '31104.fx.648.hs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.hs1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.hs1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246596
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.ht1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.jg1', '216.jh1', '324.g1', '324.eo1', '324.es1'], 'contains': ['1296.ht1', '1296.hv1', '1296.hy1', '1296.it1', '1296.iw1', '1296.jg1', '1296.jq1', '1944.cd1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [8305, 22752, 21606, 2700, 18576], 'label': '31104.fx.648.ht1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.ht1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ht1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246597
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.hu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ji1', '216.jj1', '324.h1', '324.eo1', '324.es1'], 'contains': ['1296.hv1', '1296.hw1', '1296.hx1', '1296.je1', '1296.jg1', '1296.jm1', '1296.jp1', '1944.ce1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 22752, 21606, 2700, 18576], 'label': '31104.fx.648.hu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.hu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.hu1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 186246598
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.hv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.v1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.jg1', '216.jm1', '324.g1', '324.em1', '324.ev1'], 'contains': ['1296.hz1', '1296.ie1', '1296.ik1', '1296.it2', '1296.iv1', '1296.jh1', '1296.jq1', '1944.cd1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [8305, 22752, 21678, 2628, 18576], 'label': '31104.fx.648.hv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.hv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.hv1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246599
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.hw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.jh1', '216.jm1', '324.e1', '324.en1', '324.et1'], 'contains': ['1296.ia1', '1296.if1', '1296.im1', '1296.iy1', '1296.iz1', '1296.ji1', '1296.jt1', '1944.cd1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [8305, 12096, 2670, 2628, 18576], 'label': '31104.fx.648.hw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '648.hw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.hw1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246600
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.hx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ji1', '216.jn1', '324.f1', '324.en1', '324.et1'], 'contains': ['1296.if1', '1296.ih1', '1296.il1', '1296.jd1', '1296.ji1', '1296.jk1', '1296.js1', '1944.ce1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 12096, 2670, 2628, 18576], 'label': '31104.fx.648.hx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '648.hx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.hx1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246601
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.hy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.v1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.jj1', '216.jn1', '324.h1', '324.em1', '324.ev1'], 'contains': ['1296.ie1', '1296.ii1', '1296.ij1', '1296.je2', '1296.jh1', '1296.jm1', '1296.jo1', '1944.ce1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 22752, 21678, 2628, 18576], 'label': '31104.fx.648.hy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.hy1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.hy1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246602
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.hz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.jk1', '216.jo1', '324.c1', '324.es1', '324.ev1'], 'contains': ['1296.ht1', '1296.hu1', '1296.hz1', '1296.ib1', '1296.in1', '1296.ir1', '1296.jm1', '1944.cf1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 22752, 24198, 108, 18576], 'label': '31104.fx.648.hz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.hz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.hz1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246603
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.v1'], 'contains': ['72.ch1', '72.cq1', '72.db1', '108.fm1', '108.fv1', '144.cp1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1, 10924, 12384, 18576, 15552, 18144, 18216, 1728], 'label': '31104.fx.36.db1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.db1', 'old_label': '36.db1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.db1', 'subgroup_fusion': None, 'weyl_group': '432.535'}
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id: 186246604
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.ia1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.u1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.jl1', '216.jp1', '324.d1', '324.es1', '324.ev1'], 'contains': ['1296.hu1', '1296.hx1', '1296.ib1', '1296.ij1', '1296.io1', '1296.ja1', '1296.jq1', '1944.cg1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [8305, 10368, 24198, 108, 18576], 'label': '31104.fx.648.ia1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.ia1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ia1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246605
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.ib1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.s1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.jo1', '324.a1', '324.et1'], 'contains': ['1296.ia1', '1296.ic1', '1296.ip1', '1296.ix1', '1296.jk1', '1944.cf1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [5713, 12096, 6, 108, 18576], 'label': '31104.fx.648.ib1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '648.ib1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ib1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246606
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.ic1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.w1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.jp1', '324.b1', '324.et1'], 'contains': ['1296.ic1', '1296.il1', '1296.iq1', '1296.jc1', '1296.jt1', '1944.cg1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [8305, 12096, 6, 108, 18576], 'label': '31104.fx.648.ic1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '648.ic1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ic1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246607
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.id1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['162.o1', '216.jq1', '216.js1', '324.el1'], 'contains': ['1296.jv1', '1296.kf1', '1296.km1', '1944.ci1', '2592.ew1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [19135, 2592, 36, 16080, 15984], 'label': '31104.fx.648.id1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.el1', 'old_label': '648.id1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.id1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186246608
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.ie1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['162.p1', '216.jr1', '216.jt1', '324.el1'], 'contains': ['1296.jv1', '1296.ki1', '1296.kr1', '1944.ch1', '2592.ex1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [19135, 18576, 36, 30532, 16056], 'label': '31104.fx.648.ie1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.el1', 'old_label': '648.ie1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ie1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186246609
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.if1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['162.r1', '216.ju1', '216.jv1', '216.jw1', '324.el1'], 'contains': ['1296.jv1', '1296.kz1', '1296.li1', '1944.cj1', '2592.ez1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [20737, 2592, 36, 16080, 18576], 'label': '31104.fx.648.if1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.el1', 'old_label': '648.if1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.if1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186246610
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.ig1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cp1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.jr1', '216.jx1', '216.kb1', '324.i1', '324.em1', '324.er1'], 'contains': ['1296.fx1', '1296.ge1', '1296.gx1', '1296.ie1', '1296.jw1', '1296.ka1', '1296.ko1', '1944.ch1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [29503, 10368, 36, 16056, 18576], 'label': '31104.fx.648.ig1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.ig1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ig1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246611
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.ih1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cn1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.jx1', '216.jz1', '324.j1', '324.en1', '324.ep1'], 'contains': ['1296.fy1', '1296.gi1', '1296.gy1', '1296.if1', '1296.jy1', '1296.kb1', '1296.kp1', '1944.ch1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [26047, 12096, 36, 16056, 18576], 'label': '31104.fx.648.ih1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '648.ih1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ih1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246612
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.ii1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.jx1', '216.ka1', '324.k1'], 'contains': ['1296.fz1', '1296.gj1', '1296.gz1', '1296.ig1', '1296.jz1', '1296.kc1', '1296.kq1', '1944.ch1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [26047, 12096, 36, 504, 15984], 'label': '31104.fx.648.ii1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.k1', 'old_label': '648.ii1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ii1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246613
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.ij1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.co1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.jq1', '216.jy1', '216.kd1', '324.i1', '324.eq1'], 'contains': ['1296.fx1', '1296.go1', '1296.jw2', '1296.kd1', '1296.ku1', '1944.ci1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [24198, 22752, 36, 16056, 18576], 'label': '31104.fx.648.ij1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '648.ij1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ij1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186246614
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.e1', '18.bh1'], 'contains': ['72.ct1', '108.fn1', '108.fo1', '108.fq1', '108.fw1', '108.fx1', '108.fz1', '108.ga1', '108.gc1', '108.gc2', '144.cr1'], 'core': '648.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1, 15624, 15984, 76, 22752, 15552, 18144, 5712], 'label': '31104.fx.36.dc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bh1', 'old_label': '36.dc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dc1', 'subgroup_fusion': None, 'weyl_group': '1728.47856'}
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id: 186246615
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.ik1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.co1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.jy1', '216.kc1', '324.j1', '324.k1', '324.ep1'], 'contains': ['1296.fy1', '1296.fz1', '1296.gp1', '1296.gq1', '1296.jy1', '1296.ke1', '1296.kv1', '1944.ci1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [26047, 12096, 36, 2592, 18576], 'label': '31104.fx.648.ik1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '648.ik1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ik1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
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id: 186246616
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.il1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cn1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.jt1', '216.jz1', '216.ka1', '216.kb1', '324.l1', '324.eo1', '324.eq1'], 'contains': ['1296.ga1', '1296.gf1', '1296.hn1', '1296.hv1', '1296.jw2', '1296.kh1', '1296.kk1', '1944.ch1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [19135, 22752, 36, 16056, 18576], 'label': '31104.fx.648.il1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.il1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.il1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186246617
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.im1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cq1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.js1', '216.kc1', '216.kd1', '324.l1', '324.er1'], 'contains': ['1296.ga1', '1296.hi1', '1296.jw1', '1296.kj1', '1296.kl1', '1944.ci1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [19135, 22752, 36, 18576, 2592], 'label': '31104.fx.648.im1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '648.im1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.im1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
-
id: 186246618
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.in1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.p1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ju1', '216.ke1', '216.kf1', '324.m1', '324.em1', '324.er1'], 'contains': ['1296.gb1', '1296.gg1', '1296.it2', '1296.je2', '1296.jw1', '1296.kw1', '1296.lg1', '1944.cj1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1, 10368, 36, 3024, 2592], 'label': '31104.fx.648.in1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.in1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.in1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246619
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.in2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.jv1', '216.ke1', '216.kg1', '324.m1', '324.eo1', '324.eq1'], 'contains': ['1296.gb1', '1296.gg1', '1296.it1', '1296.je1', '1296.jw2', '1296.kw2', '1296.lg2', '1944.cj1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1, 10368, 36, 18576, 2592], 'label': '31104.fx.648.in2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.in2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.in2', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246620
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.io1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.jw1', '216.ke1', '216.kh1', '324.n1'], 'contains': ['1296.gc1', '1296.gh1', '1296.iu1', '1296.jf1', '1296.jx1', '1296.kx1', '1296.lh1', '1944.cj1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [20737, 12384, 36, 18576, 2592], 'label': '31104.fx.648.io1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.n1', 'old_label': '648.io1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.io1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246621
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.ip1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.kf1', '216.kg1', '216.kh1', '324.o1', '324.en1', '324.ep1'], 'contains': ['1296.gd1', '1296.gk1', '1296.iy1', '1296.jd1', '1296.jy1', '1296.ky1', '1296.lf1', '1944.cj1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [20737, 1728, 36, 3024, 2592], 'label': '31104.fx.648.ip1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '648.ip1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ip1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246622
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.iq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cu1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ki1', '216.kl1', '324.i1', '324.p1', '324.eo1'], 'contains': ['1296.ge1', '1296.jg1', '1296.jw2', '1296.lk1', '1296.ln1', '1944.ck1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [14311, 10368, 36, 2592, 18576], 'label': '31104.fx.648.iq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '648.iq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.iq1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
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id: 186246623
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.ir1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cv1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.kj1', '216.kk1', '216.kl1', '324.l1', '324.q1', '324.em1'], 'contains': ['1296.gf1', '1296.jh1', '1296.jw1', '1296.ll1', '1296.lm1', '1944.ck1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [3943, 22752, 36, 2592, 18576], 'label': '31104.fx.648.ir1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '648.ir1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ir1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
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id: 186246624
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.is1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cu1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ki1', '216.kj1', '324.j1', '324.u1', '324.en1'], 'contains': ['1296.gi1', '1296.ji1', '1296.jy1', '1296.lo1', '1296.lq2', '1944.ck1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [25975, 12096, 36, 2592, 18576], 'label': '31104.fx.648.is1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '648.is1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.is1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
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id: 186246625
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.e1', '18.i1', '18.bf1', '18.bi1'], 'contains': ['72.cu1', '108.fn1', '108.fo1', '108.fp1', '108.fw1', '108.fy1', '108.ga1', '108.gb1', '144.cs1'], 'core': '216.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1, 15624, 15984, 76, 10368, 15552, 18144, 5712], 'label': '31104.fx.36.dd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.dd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dd1', 'subgroup_fusion': None, 'weyl_group': '3456.di'}
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id: 186246626
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.it1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cu1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ki1', '216.kk1', '324.k1', '324.t1', '324.u1'], 'contains': ['1296.gj1', '1296.jj1', '1296.jy1', '1296.lp1', '1296.lq1', '1944.ck1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [10495, 12096, 36, 18576, 2592], 'label': '31104.fx.648.it1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.t1', 'old_label': '648.it1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.it1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246627
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.iu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.dc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.km1', '216.ku1', '216.ky1', '324.w1', '324.er1', '324.es1'], 'contains': ['1296.gl1', '1296.gm1', '1296.ht1', '1296.hx1', '1296.ka1', '1296.kl1', '1296.kw1', '1944.cm1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [26485, 18576, 12138, 2592, 22752], 'label': '31104.fx.648.iu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.iu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.iu1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
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id: 186246628
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.iv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.kn1', '216.kx1', '324.i1', '324.es1', '324.ex1'], 'contains': ['1296.go1', '1296.gu1', '1296.ib1', '1296.jg1', '1296.ka1', '1296.ko1', '1296.lb1', '1944.cl1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [29503, 10368, 2628, 16056, 18576], 'label': '31104.fx.648.iv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.iv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.iv1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246629
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.iw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.kn1', '216.kv1', '324.j1', '324.et1', '324.eu1'], 'contains': ['1296.gp1', '1296.gv1', '1296.ic1', '1296.ji1', '1296.kb1', '1296.kp1', '1296.ld2', '1944.cl1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [26047, 12096, 2628, 16056, 18576], 'label': '31104.fx.648.iw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '648.iw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.iw1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246630
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.ix1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.kn1', '216.kw1', '324.k1'], 'contains': ['1296.gq1', '1296.gw1', '1296.id1', '1296.jj1', '1296.kc1', '1296.kq1', '1296.le2', '1944.cl1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [6, 12096, 18612, 432, 16056], 'label': '31104.fx.648.ix1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.k1', 'old_label': '648.ix1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ix1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246631
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.iy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.db1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.km1', '216.kz1', '324.x1', '324.ep1', '324.et1'], 'contains': ['1296.gn1', '1296.gr1', '1296.ia1', '1296.il1', '1296.kb1', '1296.kv1', '1296.ky1', '1944.cm1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26485, 12096, 12138, 2592, 18576], 'label': '31104.fx.648.iy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '648.iy1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.iy1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246632
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.iz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ee1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ko1', '216.la1', '324.w1', '324.em1', '324.ex1'], 'contains': ['1296.gs1', '1296.hd1', '1296.iv1', '1296.jo1', '1296.ka1', '1296.kw1', '1296.lm1', '1944.cn1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [26485, 18576, 12210, 2592, 22752], 'label': '31104.fx.648.iz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.iz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.iz1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
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id: 186246633
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.ja1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ec1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ko1', '216.lb1', '324.x1', '324.en1', '324.eu1'], 'contains': ['1296.gt1', '1296.hf1', '1296.iz1', '1296.js1', '1296.kb1', '1296.ky1', '1296.lq2', '1944.cn1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26485, 12096, 12210, 2592, 18576], 'label': '31104.fx.648.ja1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '648.ja1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ja1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246634
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.jb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ej1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.kp1', '216.lc1', '324.bf1', '324.en1', '324.et1'], 'contains': ['1296.ha1', '1296.he1', '1296.jk1', '1296.jt1', '1296.kb1', '1296.lf1', '1296.lo1', '1944.co1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 18576, 12210, 2592, 12096], 'label': '31104.fx.648.jb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '648.jb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.jb1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
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id: 186246635
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.jc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.em1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.kp1', '216.ld1', '324.bk1', '324.em1', '324.es1'], 'contains': ['1296.hb1', '1296.hc1', '1296.jm1', '1296.jq1', '1296.ka1', '1296.lg1', '1296.ll1', '1944.co1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 10368, 14730, 16056, 18576], 'label': '31104.fx.648.jc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '648.jc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.jc1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246636
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1', '12.v1', '18.o1'], 'contains': ['72.ci1', '72.cm1', '72.cx1', '108.fn1', '108.fr1', '108.fs1', '108.ft1', '108.fv1', '144.ct1'], 'core': '216.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1, 22752, 10368, 18576, 10924, 18144, 18216, 15552], 'label': '31104.fx.36.de1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '36.de1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.de1', 'subgroup_fusion': None, 'weyl_group': None}
-
id: 186246637
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.jd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cy1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.kq1', '216.kr1', '216.ks1', '216.lf1', '324.w1', '324.eq1', '324.ew1'], 'contains': ['1296.gl1', '1296.gm1', '1296.gs1', '1296.hd1', '1296.kd1', '1296.kk1', '1296.kw2', '1944.cp1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [26485, 18576, 12138, 16056, 22752], 'label': '31104.fx.648.jd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.jd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.jd1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
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id: 186246638
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.je1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cy1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.kq1', '216.lg1', '324.x1', '324.ep1', '324.eu1'], 'contains': ['1296.gn1', '1296.gr1', '1296.gt1', '1296.hf1', '1296.ke1', '1296.kp1', '1296.ky1', '1944.cp1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26485, 12096, 12138, 16056, 18576], 'label': '31104.fx.648.je1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '648.je1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.je1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246639
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.jf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.fa1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['162.ba1', '216.kr1', '216.lh1', '324.el1'], 'contains': ['1296.kf1', '1296.kr1', '1296.kz1', '1944.cp1', '2592.fi1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [12133, 2592, 6, 5712, 18576], 'label': '31104.fx.648.jf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ge1', 'old_label': '648.jf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.jf1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186246640
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.jg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['162.bb1', '216.ks1', '216.li1'], 'contains': ['1296.kg1', '1296.kt1', '1296.la1', '1944.cp1', '2592.fj1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [26485, 18576, 12138, 29452, 2664], 'label': '31104.fx.648.jg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ks1', 'old_label': '648.jg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.jg1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186246641
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.jh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.kt1', '216.lk1', '324.i1', '324.y1', '324.ew1'], 'contains': ['1296.gu1', '1296.gx1', '1296.kd1', '1296.lb2', '1296.ln1', '1944.cq1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [14311, 10368, 16092, 2592, 18576], 'label': '31104.fx.648.jh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '648.jh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.jh1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186246642
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.ji1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.kt1', '216.lj1', '324.k1', '324.z1', '324.ba1'], 'contains': ['1296.gw1', '1296.gz1', '1296.ke1', '1296.ld1', '1296.lq1', '1944.cq1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [10495, 12096, 15588, 18576, 2592], 'label': '31104.fx.648.ji1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.t1', 'old_label': '648.ji1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ji1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246643
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.ji2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.kt1', '216.lj2', '324.j1', '324.ba1', '324.eu1'], 'contains': ['1296.gv1', '1296.gy1', '1296.ke1', '1296.ld2', '1296.lq2', '1944.cq1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [25975, 12096, 108, 2592, 18576], 'label': '31104.fx.648.ji2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '648.ji2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ji2', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186246644
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.jj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.kv1', '216.kw1', '216.kx1', '324.l1', '324.ev1', '324.ew1'], 'contains': ['1296.hi1', '1296.hm1', '1296.hu1', '1296.jh1', '1296.kh1', '1296.kk1', '1296.lb2', '1944.cl1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [19135, 22752, 2628, 16056, 18576], 'label': '31104.fx.648.jj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.jj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.jj1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246645
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.jk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.fc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['162.bd1', '216.ku1', '216.lm1', '324.el1'], 'contains': ['1296.ki1', '1296.km1', '1296.kz1', '1944.cm1', '2592.fn1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [7477, 18576, 6, 5260, 2664], 'label': '31104.fx.648.jk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.gd1', 'old_label': '648.jk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.jk1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186246646
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.jl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.db1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ky1', '216.kz1', '216.lm1', '324.bg1', '324.eq1', '324.ev1'], 'contains': ['1296.hj1', '1296.hk1', '1296.hz1', '1296.ij1', '1296.kh1', '1296.ku1', '1296.kw2', '1944.cm1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26485, 10368, 12138, 2592, 18576], 'label': '31104.fx.648.jl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '648.jl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.jl1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246647
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.e1', '12.w1', '18.p1', '18.bg1', '18.bj1'], 'contains': ['72.b1', '108.fo1', '108.fp1', '108.fq1', '108.fr1', '108.fu1', '144.cv1', '144.fu1'], 'core': '72.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1, 16056, 432, 5712, 10368, 15552, 2592, 22752], 'label': '31104.fx.36.df1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '36.df1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.df1', 'subgroup_fusion': None, 'weyl_group': '10368.je'}
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id: 186246648
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.jm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ec1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.la1', '216.lb1', '324.bg1', '324.eo1', '324.ew1'], 'contains': ['1296.hl1', '1296.hq1', '1296.iw1', '1296.jp1', '1296.kh1', '1296.kw2', '1296.ln1', '1944.cn1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26485, 10368, 12210, 2592, 18576], 'label': '31104.fx.648.jm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '648.jm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.jm1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246649
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.jn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cz1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.le1', '216.ll1', '324.bf1', '324.ep1', '324.eu1'], 'contains': ['1296.ha1', '1296.he1', '1296.hg1', '1296.hh1', '1296.kb1', '1296.ke1', '1296.lf1', '1944.cr1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 18576, 12138, 2592, 12096], 'label': '31104.fx.648.jn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '648.jn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.jn1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
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id: 186246650
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.jo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ej1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.lc1', '216.ld1', '324.bk1', '324.eo1', '324.ev1'], 'contains': ['1296.ho1', '1296.hp1', '1296.jm1', '1296.jq1', '1296.kh1', '1296.lg2', '1296.lk1', '1944.co1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 10368, 12210, 2592, 18576], 'label': '31104.fx.648.jo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '648.jo1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.jo1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246651
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.jp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cz1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.le1', '216.lo1', '216.lp1', '324.bk1', '324.eq1', '324.ew1'], 'contains': ['1296.hb1', '1296.hc1', '1296.hr1', '1296.hs1', '1296.kd1', '1296.kh1', '1296.lg2', '1944.cr1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 10368, 12138, 2592, 18576], 'label': '31104.fx.648.jp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '648.jp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.jp1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246652
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.jq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['162.bg1', '216.ln1', '216.lp1', '324.el1'], 'contains': ['1296.kf1', '1296.ki1', '1296.li1', '1944.cr1', '2592.fr1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [1, 2592, 12138, 5712, 18576], 'label': '31104.fx.648.jq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.el1', 'old_label': '648.jq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.jq1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 186246653
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.jr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.dd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.lf1', '216.lg1', '216.lh1', '216.li1', '324.bg1', '324.er1', '324.ex1'], 'contains': ['1296.hj1', '1296.hk1', '1296.hl1', '1296.hq1', '1296.kj1', '1296.ko1', '1296.kw1', '1944.cp1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26485, 10368, 12138, 16056, 18576], 'label': '31104.fx.648.jr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '648.jr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.jr1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 186246654
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.js1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.lj1', '216.lj2', '216.lk1', '324.l1', '324.bh1', '324.ex1'], 'contains': ['1296.hm1', '1296.hn1', '1296.kj1', '1296.lb1', '1296.lm1', '1944.cq1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [3943, 22752, 16092, 2592, 18576], 'label': '31104.fx.648.js1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '648.js1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.js1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
-
id: 186246655
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.jt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.de1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ll1', '216.ln1', '216.lo1', '324.bk1', '324.er1', '324.ex1'], 'contains': ['1296.ho1', '1296.hp1', '1296.hr1', '1296.hs1', '1296.ka1', '1296.kj1', '1296.lg1', '1944.cr1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 10368, 12138, 16056, 18576], 'label': '31104.fx.648.jt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '648.jt1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.jt1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 186246656
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.ju1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.eb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.lq1', '216.lr1', '324.w1', '324.eo1', '324.ev1'], 'contains': ['1296.ht1', '1296.hx1', '1296.iv1', '1296.jo1', '1296.kk1', '1296.kw2', '1296.lk1', '1944.cs1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [26485, 18576, 14730, 16056, 22752], 'label': '31104.fx.648.ju1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.ju1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ju1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
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id: 186246657
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.jv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ls1', '216.lt1', '324.bv1', '324.eo1', '324.ew1'], 'contains': ['1296.hw1', '1296.hy1', '1296.jn1', '1296.jr1', '1296.kk1', '1296.lg2', '1296.ln1', '1944.ct1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 22752, 2598, 16056, 18576], 'label': '31104.fx.648.jv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.jv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.jv1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246658
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1'], 'contains': ['72.dc1', '108.fs1', '108.fu1', '108.fv1', '108.fw1', '108.fx1', '108.ga1', '108.gb1', '108.gc1', '108.gc2', '144.cw1', '144.cx1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1, 15624, 15984, 76, 12384, 15552, 18144, 5712], 'label': '31104.fx.36.dg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.dg1', 'old_label': '36.dg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dg1', 'subgroup_fusion': None, 'weyl_group': '864.4679'}
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id: 186246659
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.jw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.lu1', '216.lv1', '216.lw1', '324.l1', '324.bl1', '324.es1'], 'contains': ['1296.hu1', '1296.hv1', '1296.kl1', '1296.lb1', '1296.ll1', '1944.cu1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [19135, 22752, 16092, 2592, 18576], 'label': '31104.fx.648.jw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '648.jw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.jw1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186246660
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.jx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ef1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.lq1', '216.lx1', '324.bg1', '324.em1', '324.es1'], 'contains': ['1296.hz1', '1296.ij1', '1296.iw1', '1296.jp1', '1296.ko1', '1296.kw1', '1296.ll1', '1944.cs1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26485, 10368, 14730, 16056, 18576], 'label': '31104.fx.648.jx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '648.jx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.jx1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246661
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.jy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.eb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.lr1', '216.lx1', '324.x1', '324.en1', '324.et1'], 'contains': ['1296.ia1', '1296.il1', '1296.iz1', '1296.js1', '1296.kp1', '1296.ky1', '1296.lo1', '1944.cs1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26485, 12096, 14730, 16056, 18576], 'label': '31104.fx.648.jy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '648.jy1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.jy1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246662
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.jz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ls1', '216.ly1', '324.bw1', '324.en1', '324.eu1'], 'contains': ['1296.ih1', '1296.im1', '1296.jl1', '1296.ju1', '1296.kp1', '1296.lf1', '1296.lq2', '1944.ct1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 12096, 78, 2592, 18576], 'label': '31104.fx.648.jz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '648.jz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.jz1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246663
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.ka1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.v1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.lt1', '216.ly1', '324.bv1', '324.em1', '324.ex1'], 'contains': ['1296.ii1', '1296.ik1', '1296.jn1', '1296.jr1', '1296.ko1', '1296.lg1', '1296.lm1', '1944.ct1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 10368, 2598, 16056, 18576], 'label': '31104.fx.648.ka1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.ka1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ka1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246664
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.kb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.n1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.mb1', '216.mc1', '216.md1', '324.bv1', '324.er1', '324.es1'], 'contains': ['1296.hw1', '1296.hy1', '1296.in1', '1296.io1', '1296.kl1', '1296.ko1', '1296.lg1', '1944.cv1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 10368, 6, 16056, 18576], 'label': '31104.fx.648.kb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.kb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.kb1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246665
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.kc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['162.bi1', '216.lz1', '216.mc1', '324.el1'], 'contains': ['1296.km1', '1296.kr1', '1296.li1', '1944.cv1', '2592.ft1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [5713, 18576, 6, 5260, 2664], 'label': '31104.fx.648.kc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.el1', 'old_label': '648.kc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.kc1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186246666
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.kd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['162.bj1', '216.ma1', '216.mc1'], 'contains': ['1296.kn1', '1296.ks1', '1296.lj1', '1944.cv1', '2592.fu1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [5713, 18576, 6, 15628, 2664], 'label': '31104.fx.648.kd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.kd1', 'old_label': '648.kd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.kd1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186246667
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.ke1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.lw1', '216.me1', '324.i1', '324.bo1', '324.ev1'], 'contains': ['1296.ib1', '1296.ie1', '1296.ku1', '1296.lb2', '1296.lk1', '1944.cu1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [29503, 10368, 16092, 2592, 18576], 'label': '31104.fx.648.ke1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '648.ke1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ke1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186246668
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.kf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.lu1', '216.me1', '324.j1', '324.bq1', '324.et1'], 'contains': ['1296.ic1', '1296.if1', '1296.kv1', '1296.ld2', '1296.lo1', '1944.cu1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [26047, 12096, 108, 2592, 18576], 'label': '31104.fx.648.kf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '648.kf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.kf1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186246669
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '6.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.c1', '3.b1'], 'contains': ['12.b1', '12.n1', '12.r1', '18.w1', '18.ba1', '18.bb1', '24.u1'], 'core': '12.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [10405, 2592, 1728, 10368, 15552, 12138, 16080, 432, 16056, 22752], 'label': '31104.fx.6.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '6.i1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.i1', 'subgroup_fusion': None, 'weyl_group': '3456.gu'}
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id: 186246670
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1', '18.j1'], 'contains': ['72.de1', '108.fs1', '108.ft1', '108.fu1', '108.fw1', '108.fx1', '108.fy1', '108.fz1', '144.cy1', '144.cz1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1, 15624, 15984, 20812, 12384, 15552, 18144, 5712], 'label': '31104.fx.36.dh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1', 'old_label': '36.dh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dh1', 'subgroup_fusion': None, 'weyl_group': '1728.47859'}
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id: 186246671
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.kg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.lv1', '216.me1', '324.k1', '324.bp1', '324.bq1'], 'contains': ['1296.id1', '1296.ig1', '1296.kv1', '1296.ld1', '1296.lp1', '1944.cu1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [26047, 12096, 15588, 18576, 2592], 'label': '31104.fx.648.kg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.t1', 'old_label': '648.kg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.kg1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246672
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.kh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.lz1', '216.ma1', '216.mb1', '216.mf1', '324.bv1', '324.eq1', '324.ev1'], 'contains': ['1296.ii1', '1296.ik1', '1296.in1', '1296.io1', '1296.kk1', '1296.ku1', '1296.lg2', '1944.cv1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 22752, 6, 16056, 18576], 'label': '31104.fx.648.kh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.kh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.kh1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246673
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.ki1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.md1', '216.mf1', '324.bw1', '324.ep1', '324.et1'], 'contains': ['1296.ih1', '1296.im1', '1296.ip1', '1296.iq1', '1296.kp1', '1296.kv1', '1296.lf1', '1944.cv1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 12096, 6, 2592, 18576], 'label': '31104.fx.648.ki1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '648.ki1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ki1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 186246674
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.kj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.mg1', '216.mh1', '324.m1', '324.es1', '324.ex1'], 'contains': ['1296.ir1', '1296.it1', '1296.ja1', '1296.je1', '1296.kw1', '1296.lb1', '1296.lg1', '1944.cw1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1, 10368, 15588, 3024, 2592], 'label': '31104.fx.648.kj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.kj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.kj1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 186246675
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.kj2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.mg1', '216.mi1', '324.m1', '324.ev1', '324.ew1'], 'contains': ['1296.ir1', '1296.it2', '1296.ja1', '1296.je2', '1296.kw2', '1296.lb2', '1296.lg2', '1944.cw1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1, 10368, 15588, 18576, 2592], 'label': '31104.fx.648.kj2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.kj2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.kj2', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246676
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.kk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.mg1', '216.mj1', '324.n1'], 'contains': ['1296.is1', '1296.iu1', '1296.jb1', '1296.jf1', '1296.kx1', '1296.lc1', '1296.lh1', '1944.cw1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [20737, 12384, 15588, 18576, 2592], 'label': '31104.fx.648.kk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.n1', 'old_label': '648.kk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.kk1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246677
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.kl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.mh1', '216.mi1', '216.mj1', '324.o1', '324.et1', '324.eu1'], 'contains': ['1296.ix1', '1296.iy1', '1296.jc1', '1296.jd1', '1296.ky1', '1296.ld2', '1296.lf1', '1944.cw1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [20737, 1728, 15588, 3024, 2592], 'label': '31104.fx.648.kl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '648.kl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.kl1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246678
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.km1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.mk1', '216.mn1', '324.p1', '324.y1', '324.bo1'], 'contains': ['1296.lb2', '1296.lk1', '1296.ln1', '1944.cx1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [13951, 10368, 16092, 18576, 2592], 'label': '31104.fx.648.km1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.s1', 'old_label': '648.km1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.km1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246679
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.kn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ml1', '216.mm1', '216.mm2', '216.mn1', '324.q1', '324.bh1', '324.bl1'], 'contains': ['1296.lb1', '1296.ll1', '1296.lm1', '1944.cx1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [3583, 22752, 16092, 18576, 2592], 'label': '31104.fx.648.kn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.u1', 'old_label': '648.kn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.kn1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246680
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.ko1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.mk1', '216.ml1', '324.u1', '324.z1', '324.bq1'], 'contains': ['1296.ld1', '1296.lo1', '1296.lq1', '1944.cx1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [10423, 12096, 15588, 15984, 18576], 'label': '31104.fx.648.ko1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.t1', 'old_label': '648.ko1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ko1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246681
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['9.b1', '12.x1'], 'contains': ['72.ea1', '72.ec1', '72.eg1', '72.el1', '72.ev1', '72.ex1', '72.fd1', '108.ge1', '108.gi1', '144.fy1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [5713, 12096, 22752, 6, 5260, 18576, 2664, 36], 'label': '31104.fx.36.di1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.di1', 'old_label': '36.di1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.di1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
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id: 186246682
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.kp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.mk1', '216.mm1', '324.u1', '324.ba1', '324.bp1'], 'contains': ['1296.ld1', '1296.lp1', '1296.lq2', '1944.cx1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [25975, 12096, 15588, 2592, 18576], 'label': '31104.fx.648.kp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.t1', 'old_label': '648.kp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.kp1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246683
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '648.kp2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.mk1', '216.mm2', '324.t1', '324.ba1', '324.bq1'], 'contains': ['1296.ld2', '1296.lp1', '1296.lq1', '1944.cx1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [10495, 12096, 108, 2592, 18576], 'label': '31104.fx.648.kp2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.t1', 'old_label': '648.kp2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.kp2', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186246684
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.a1', '432.a1', '432.l1', '432.l2', '432.s1', '432.el1', '432.em1', '432.hk1'], 'contains': ['1728.a1', '1728.n1', '1728.o1', '2592.a1', '2592.d1', '2592.e1', '2592.g1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [16056, 15552, 12096, 22752], 'label': '31104.fx.864.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1', 'old_label': '864.a1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186246685
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.a1', '432.b1', '432.i1', '432.m1', '432.t1', '432.z1', '432.el1', '432.hk1'], 'contains': ['1728.a1', '1728.o1', '2592.a1', '2592.f1', '2592.g1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [504, 3096, 12096, 22752], 'label': '31104.fx.864.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '864.b1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186246686
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.a1', '432.c1', '432.h1', '432.n1', '432.u1', '432.bc1', '432.en1', '432.hn1'], 'contains': ['1728.d1', '1728.p1', '2592.a1', '2592.b1', '2592.c1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [16056, 15552, 22752, 10368], 'label': '31104.fx.864.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '864.c1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186246687
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.a1', '432.d1', '432.o1', '432.v1', '432.ep1', '432.hq1'], 'contains': ['1728.f1', '1728.q1', '1728.r1', '2592.b1', '2592.d1', '2592.g1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [15552, 504, 12096, 12384], 'label': '31104.fx.864.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1', 'old_label': '864.d1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186246688
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.a1', '432.e1', '432.j1', '432.p1', '432.w1', '432.ba1', '432.eo1', '432.hq1'], 'contains': ['1728.e1', '1728.r1', '2592.b1', '2592.e1', '2592.f1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [2592, 18648, 12096, 12384], 'label': '31104.fx.864.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '864.e1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.e1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186246689
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.a1', '432.f1', '432.k1', '432.q1', '432.x1', '432.bb1', '432.ep1', '432.ho1'], 'contains': ['1728.g1', '1728.q1', '2592.c1', '2592.d1', '2592.f1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [18576, 18144, 12096, 12384], 'label': '31104.fx.864.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '864.f1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.f1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186246690
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.a1', '432.g1', '432.r1', '432.r2', '432.y1', '432.eo1', '432.ep1', '432.hp1'], 'contains': ['1728.g1', '1728.r1', '2592.c1', '2592.e1', '2592.g1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [16056, 18216, 12096, 12384], 'label': '31104.fx.864.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1', 'old_label': '864.g1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186246691
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ck1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ew1', '288.b1', '432.bd1', '432.bg1', '432.er1'], 'contains': ['1728.b1', '1728.t1', '1728.cr1', '2592.h1', '2592.i1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [36, 3096, 12940, 10368], 'label': '31104.fx.864.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.eb1', 'old_label': '864.h1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.h1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186246692
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['9.c1', '12.x1'], 'contains': ['72.eb1', '72.ee1', '72.ef1', '72.er1', '72.eu1', '72.ey1', '72.fb1', '108.gd1', '108.ge1', '108.gk1', '144.fz1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [1, 22752, 10368, 24198, 16080, 2592, 18576, 36], 'label': '31104.fx.36.dj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.dj1', 'old_label': '36.dj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dj1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
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id: 186246693
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ck1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.ex1', '288.b1', '432.be1', '432.bh1', '432.ev1'], 'contains': ['1728.h1', '1728.w1', '1728.cs1', '2592.h1', '2592.k1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [36, 3096, 10924, 2016], 'label': '31104.fx.864.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ef1', 'old_label': '864.i1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.i1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 186246694
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ck1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.ey1', '288.b1', '288.c1', '288.d1', '432.bf1', '432.bi1', '432.ew1'], 'contains': ['1728.i1', '1728.x1', '1728.ct1', '2592.h1', '2592.j1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [36, 3096, 556, 12384], 'label': '31104.fx.864.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.eg1', 'old_label': '864.j1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.j1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 186246695
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.e1', '432.a1', '432.b1', '432.bk1', '432.bn1', '432.cv1', '432.cw1', '432.fb1'], 'contains': ['1728.a1', '1728.z1', '1728.cu1', '2592.i1', '2592.l1', '2592.m1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [36, 18144, 12096, 22752], 'label': '31104.fx.864.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.be1', 'old_label': '864.k1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.k1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246696
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.ea1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.b1', '288.e1', '432.c1', '432.bj1', '432.bo1', '432.cx1', '432.fc1'], 'contains': ['1728.d1', '1728.ba1', '1728.cv1', '2592.i1', '2592.j1', '2592.k1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [36, 18144, 22752, 10368], 'label': '31104.fx.864.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '864.l1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.l1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 186246697
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.c1', '288.e1', '432.e1', '432.bl1', '432.bp1', '432.cy1', '432.fd1'], 'contains': ['1728.e1', '1728.bb1', '1728.cw1', '2592.j1', '2592.l1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [36, 18648, 12096, 12384], 'label': '31104.fx.864.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.r1', 'old_label': '864.m1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.m1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
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id: 186246698
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.d1', '288.e1', '432.d1', '432.cz1', '432.fd1'], 'contains': ['1728.f1', '1728.bb1', '1728.cw2', '2592.j1', '2592.m1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [36, 3096, 12096, 12384], 'label': '31104.fx.864.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bp1', 'old_label': '864.n1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.n1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
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id: 186246699
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.e1', '432.f1', '432.g1', '432.bm1', '432.bq1', '432.cy1', '432.cz1', '432.fe1'], 'contains': ['1728.g1', '1728.bb1', '1728.cw3', '2592.k1', '2592.l1', '2592.m1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [36, 18144, 12096, 12384], 'label': '31104.fx.864.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '864.o1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.o1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246700
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.di1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.f1', '288.g1', '288.h1', '432.h1', '432.bj1', '432.br1', '432.bs1', '432.bt1', '432.di1', '432.ff1'], 'contains': ['1728.d1', '1728.cd1', '2592.n1', '2592.o1', '2592.p1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [10405, 18144, 22752, 10368], 'label': '31104.fx.864.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cr1', 'old_label': '864.p1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.p1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186246701
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.f1', '432.i1', '432.bk1', '432.bx1', '432.ca1', '432.cd1', '432.dj1', '432.fg1'], 'contains': ['1728.a1', '1728.ce1', '2592.n1', '2592.q1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [10405, 18144, 22752, 1728], 'label': '31104.fx.864.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bc1', 'old_label': '864.q1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.q1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246702
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.fg1', '288.g1', '432.bd1', '432.bu1', '432.fh1'], 'contains': ['1728.b1', '1728.cf1', '2592.n1', '2592.r1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [10405, 15552, 10368, 12940], 'label': '31104.fx.864.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bj1', 'old_label': '864.r1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.r1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246723
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.fx1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.j1', '288.n1', '432.u1', '432.bs1', '432.cq1', '432.dn1', '432.fc1'], 'contains': ['1728.d1', '1728.cv1', '2592.z1', '2592.ba1', '2592.bb1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [108, 18144, 22752, 10368], 'label': '31104.fx.864.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '864.bi1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bi1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
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id: 186246703
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.b1'], 'contains': ['72.dg1', '72.dh1', '72.dk1', '72.dl1', '72.dq1', '72.dr1', '72.dw1', '72.dx1', '72.eh1', '72.ej1', '72.ek1', '72.eo1', '72.ep1', '72.ez1', '72.fa1', '108.gf1', '108.gg1', '108.gh1'], 'core': '576.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [5713, 18576, 12096, 2598, 16056, 10368, 22752, 36], 'label': '31104.fx.36.dk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '36.dk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dk1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
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id: 186246704
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.fh1', '288.h1', '432.fl1'], 'contains': ['1728.c1', '1728.ci1', '2592.n1', '2592.s1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [10405, 18144, 10368, 29404], 'label': '31104.fx.864.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.bv1', 'old_label': '864.s1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.s1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186246705
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.f1', '288.i1', '432.j1', '432.bl1', '432.by1', '432.cb1', '432.ce1', '432.dk1', '432.fo1'], 'contains': ['1728.e1', '1728.ck1', '2592.o1', '2592.q1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [10405, 15552, 12384, 1728], 'label': '31104.fx.864.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bc1', 'old_label': '864.t1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.t1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246706
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.f1', '432.k1', '432.bm1', '432.bz1', '432.cc1', '432.cf1', '432.dk1', '432.fp1'], 'contains': ['1728.g1', '1728.ck1', '2592.p1', '2592.q1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [10405, 18144, 12384, 1728], 'label': '31104.fx.864.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bc1', 'old_label': '864.u1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.u1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246707
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.fk1', '288.g1', '432.be1', '432.bv1', '432.fq1'], 'contains': ['1728.h1', '1728.cl1', '2592.p1', '2592.r1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [10405, 15552, 2016, 12940], 'label': '31104.fx.864.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bj1', 'old_label': '864.v1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.v1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246708
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.fl1', '288.g1', '288.i1', '432.bf1', '432.bw1', '432.fr1'], 'contains': ['1728.i1', '1728.cm1', '2592.o1', '2592.r1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [10405, 15552, 12384, 12940], 'label': '31104.fx.864.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bj1', 'old_label': '864.w1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.w1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186246709
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.fm1', '288.h1', '288.i1', '432.fw1'], 'contains': ['1728.k1', '1728.co2', '2592.o1', '2592.s1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [10405, 18144, 2016, 29404], 'label': '31104.fx.864.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.bv1', 'old_label': '864.x1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.x1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186246710
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.fn1', '288.h1', '432.fx1'], 'contains': ['1728.m1', '1728.co1', '2592.p1', '2592.s1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [10405, 18144, 12384, 29404], 'label': '31104.fx.864.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.bv1', 'old_label': '864.y1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.y1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186246711
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ck1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.fo1', '288.j1', '432.bu1', '432.cg1', '432.er1'], 'contains': ['1728.b1', '1728.cr1', '2592.t1', '2592.z1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [15588, 3096, 21292, 22752], 'label': '31104.fx.864.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.eb1', 'old_label': '864.z1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.z1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186246712
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ck1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.fp1', '288.j1', '432.bv1', '432.ch1', '432.ev1'], 'contains': ['1728.h1', '1728.cs1', '2592.t1', '2592.bb1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [15588, 3096, 10924, 2016], 'label': '31104.fx.864.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ef1', 'old_label': '864.ba1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ba1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186246713
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ck1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.fq1', '288.j1', '288.k1', '288.l1', '432.bw1', '432.ci1', '432.ew1'], 'contains': ['1728.i1', '1728.ct1', '2592.t1', '2592.ba1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [15588, 3096, 556, 12384], 'label': '31104.fx.864.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.eg1', 'old_label': '864.bb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bb1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186246714
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.x1', '18.b1'], 'contains': ['72.dg1', '72.dh1', '72.di1', '72.dj1', '72.do1', '72.dp1', '72.ds1', '72.dt1', '72.eh1', '72.ei1', '72.ej1', '72.en1', '72.eq1', '72.ew1', '72.ff1', '108.gi1', '108.gj1', '108.gk1'], 'core': '576.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [5713, 18576, 12096, 6, 16056, 10368, 22752, 36], 'label': '31104.fx.36.dl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '36.dl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dl1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
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id: 186246715
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.m1', '432.l1', '432.m1', '432.s1', '432.cw1', '432.dl1', '432.dm1', '432.gg1'], 'contains': ['1728.a1', '1728.cu1', '1728.cx1', '2592.u1', '2592.x1', '2592.y1', '2592.y2'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [15588, 18144, 12096, 22752], 'label': '31104.fx.864.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.du1', 'old_label': '864.bc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bc1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 186246716
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.bc2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.m1', '432.l2', '432.t1', '432.bx1', '432.cj1', '432.cv1', '432.dm1', '432.gg1'], 'contains': ['1728.a1', '1728.cu1', '1728.cx2', '2592.u1', '2592.x2', '2592.y1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [15588, 18144, 12096, 10368], 'label': '31104.fx.864.bc2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.be1', 'old_label': '864.bc2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bc2', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246717
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.bd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.m1', '432.n1', '432.u1', '432.br1', '432.ck1', '432.cx1', '432.dn1', '432.gh1'], 'contains': ['1728.d1', '1728.cv1', '1728.cy1', '2592.u1', '2592.v1', '2592.w1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [3132, 18144, 22752, 10368], 'label': '31104.fx.864.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bd1', 'old_label': '864.bd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bd1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 186246718
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.m1', '432.p1', '432.w1', '432.by1', '432.cl1', '432.cy1', '432.do1', '432.gi1'], 'contains': ['1728.e1', '1728.cw3', '1728.cz1', '2592.v1', '2592.x1', '2592.x2'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [108, 18648, 12096, 12384], 'label': '31104.fx.864.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '864.be1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.be1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246719
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.m1', '432.o1', '432.v1', '432.cz1', '432.dp1', '432.gi1'], 'contains': ['1728.f1', '1728.cw3', '1728.cz2', '2592.v1', '2592.y1', '2592.y2'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [108, 3096, 12096, 12384], 'label': '31104.fx.864.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.dw1', 'old_label': '864.bf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bf1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 186246720
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.m1', '432.q1', '432.r2', '432.y1', '432.cz1', '432.do2', '432.dp2', '432.gj2'], 'contains': ['1728.g1', '1728.cw2', '1728.cz2', '2592.w1', '2592.x1', '2592.y1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [15588, 18144, 12096, 12384], 'label': '31104.fx.864.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.dw1', 'old_label': '864.bg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bg1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 186246721
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.bg2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.m1', '432.r1', '432.x1', '432.bz1', '432.cm1', '432.cy1', '432.dp2', '432.gj1'], 'contains': ['1728.g1', '1728.cw1', '1728.cz1', '2592.w1', '2592.x2', '2592.y2'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [18684, 18144, 12096, 12384], 'label': '31104.fx.864.bg2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '864.bg2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bg2', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246722
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.n1', '432.s1', '432.t1', '432.ca1', '432.cn1', '432.dl1', '432.dm1', '432.fb1'], 'contains': ['1728.a1', '1728.cu1', '2592.z1', '2592.bc1', '2592.bd1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [108, 18144, 12096, 10368], 'label': '31104.fx.864.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.be1', 'old_label': '864.bh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bh1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246724
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.k1', '288.n1', '432.w1', '432.cb1', '432.co1', '432.do2', '432.fd1'], 'contains': ['1728.e1', '1728.cw2', '2592.ba1', '2592.bc1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [15588, 18648, 12096, 12384], 'label': '31104.fx.864.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.r1', 'old_label': '864.bj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bj1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
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id: 186246725
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.b1'], 'contains': ['72.dm1', '72.dn1', '72.do1', '72.dp1', '72.dw1', '72.dx1', '72.dy1', '72.dz1', '72.em1', '72.en1', '72.ep1', '72.ez1', '72.fc1', '72.ff1', '72.fg1', '108.gl1', '108.gm1', '108.gn1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [5713, 18576, 12096, 6, 16056, 10368, 22752, 2628], 'label': '31104.fx.36.dm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '36.dm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dm1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
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id: 186246726
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.l1', '288.n1', '432.v1', '432.dp2', '432.fd1'], 'contains': ['1728.f1', '1728.cw1', '1728.cw2', '2592.ba1', '2592.bd1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [18684, 3096, 12096, 12384], 'label': '31104.fx.864.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bp1', 'old_label': '864.bk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bk1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
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id: 186246727
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.n1', '432.x1', '432.y1', '432.cc1', '432.cp1', '432.do1', '432.dp1', '432.fe1'], 'contains': ['1728.g1', '1728.cw3', '2592.bb1', '2592.bc1', '2592.bd1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [18252, 18144, 12096, 12384], 'label': '31104.fx.864.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '864.bl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bl1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246728
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.o1', '432.a1', '432.l2', '432.m1', '432.dm1', '432.dq1', '432.dr1', '432.gg1'], 'contains': ['1728.a1', '1728.cx1', '1728.cx2', '2592.be1', '2592.bh1', '2592.bi1', '2592.bi2'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [18612, 18144, 12096, 22752], 'label': '31104.fx.864.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.du1', 'old_label': '864.bm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bm1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 186246729
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.bm2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.o1', '432.b1', '432.l1', '432.cd1', '432.cr1', '432.dl1', '432.dr1', '432.gg1'], 'contains': ['1728.a1', '1728.cx1', '2592.be1', '2592.bh2', '2592.bi1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [15660, 18144, 12096, 10368], 'label': '31104.fx.864.bm2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.be1', 'old_label': '864.bm2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bm2', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246730
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.o1', '432.c1', '432.n1', '432.bt1', '432.cu1', '432.dn1', '432.ds1', '432.gh1'], 'contains': ['1728.d1', '1728.cy1', '2592.be1', '2592.bf1', '2592.bg1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [18612, 18144, 22752, 10368], 'label': '31104.fx.864.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bd1', 'old_label': '864.bn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bn1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
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id: 186246731
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.o1', '432.e1', '432.p1', '432.ce1', '432.cs1', '432.do2', '432.dt1', '432.gi1'], 'contains': ['1728.e1', '1728.cz2', '2592.bf1', '2592.bh1', '2592.bh2'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [15660, 18648, 12096, 12384], 'label': '31104.fx.864.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '864.bo1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bo1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246732
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.o1', '432.d1', '432.o1', '432.dp2', '432.du1', '432.gi1'], 'contains': ['1728.f1', '1728.cz1', '1728.cz2', '2592.bf1', '2592.bi1', '2592.bi2'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [18612, 3096, 12096, 12384], 'label': '31104.fx.864.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.dw1', 'old_label': '864.bp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bp1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 186246733
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.o1', '432.f1', '432.r2', '432.cf1', '432.ct1', '432.do1', '432.du1', '432.gj1'], 'contains': ['1728.g1', '1728.cz1', '2592.bg1', '2592.bh2', '2592.bi2'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [468, 18144, 12096, 12384], 'label': '31104.fx.864.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '864.bq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bq1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 186246734
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.bq2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.o1', '432.g1', '432.q1', '432.r1', '432.dp1', '432.dt1', '432.du1', '432.gj2'], 'contains': ['1728.g1', '1728.cz2', '2592.bg1', '2592.bh1', '2592.bi1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [16020, 18144, 12096, 12384], 'label': '31104.fx.864.bq2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.dw1', 'old_label': '864.bq2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bq2', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 186246735
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.p1', '432.z1', '432.bk1', '432.bx1', '432.cn1', '432.cr1', '432.dv1', '432.gk1'], 'contains': ['1728.a1', '1728.da1', '2592.bj1', '2592.bk1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1, 18144, 1728, 10368], 'label': '31104.fx.864.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cs1', 'old_label': '864.br1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.br1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246736
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '36.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.b1'], 'contains': ['72.dm1', '72.dn1', '72.dq1', '72.dr1', '72.ds1', '72.dt1', '72.du1', '72.dv1', '72.em1', '72.eo1', '72.eq1', '72.et1', '72.ew1', '72.fa1', '72.fg1', '108.go1', '108.gp1', '108.gq1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [5713, 18576, 12096, 2598, 16056, 10368, 22752, 2628], 'label': '31104.fx.36.dn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '36.dn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dn1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
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id: 186246737
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.p1', '288.q1', '288.r1', '432.ba1', '432.bl1', '432.by1', '432.co1', '432.cs1', '432.dw1', '432.gl1'], 'contains': ['1728.e1', '1728.db1', '2592.bj1', '2592.bl1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1, 15552, 1728, 12384], 'label': '31104.fx.864.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cu1', 'old_label': '864.bs1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bs1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246738
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.p1', '432.bb1', '432.bm1', '432.bz1', '432.cp1', '432.ct1', '432.dw1', '432.gm1'], 'contains': ['1728.g1', '1728.db1', '2592.bj1', '2592.bm1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1, 18144, 1728, 12384], 'label': '31104.fx.864.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ct1', 'old_label': '864.bt1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bt1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246739
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.fz1', '288.s1', '432.bd1', '432.cg1', '432.gn1'], 'contains': ['1728.b1', '1728.dc1', '2592.bk1', '2592.bn1', '2592.bo1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [1, 15552, 10924, 10368], 'label': '31104.fx.864.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.eb1', 'old_label': '864.bu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bu1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186246740
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.dc1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.p1', '288.s1', '432.bc1', '432.bj1', '432.br1', '432.cq1', '432.cu1', '432.dx1', '432.gs1'], 'contains': ['1728.d1', '1728.dg1', '2592.bk1', '2592.bl1', '2592.bm1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1, 18144, 22752, 10368], 'label': '31104.fx.864.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bc1', 'old_label': '864.bv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bv1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
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id: 186246741
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.gb1', '288.s1', '432.be1', '432.ch1', '432.gt1'], 'contains': ['1728.h1', '1728.dh1', '2592.bm1', '2592.bn1', '2592.bo1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1, 15552, 10924, 2016], 'label': '31104.fx.864.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ef1', 'old_label': '864.bw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bw1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186246742
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.gc1', '288.q1', '288.s1', '432.bf1', '432.ci1', '432.gu1'], 'contains': ['1728.i1', '1728.di1', '2592.bl1', '2592.bn1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [1, 15552, 556, 12384], 'label': '31104.fx.864.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bn1', 'old_label': '864.bx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bx1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
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id: 186246744
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.t1', '432.i1', '432.bn1', '432.cj1', '432.cn1', '432.cr1', '432.dz1', '432.fg1'], 'contains': ['1728.a1', '2592.bp1', '2592.bv1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [26029, 22752, 18144, 1728], 'label': '31104.fx.864.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bc1', 'old_label': '864.bz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bz1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246745
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.u1', '432.z1', '432.bn1', '432.ca1', '432.cd1', '432.cj1', '432.eb1', '432.gk1'], 'contains': ['1728.a1', '2592.bq1', '2592.bw1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [15625, 1728, 18144, 10368], 'label': '31104.fx.864.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cs1', 'old_label': '864.ca1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ca1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246746
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.gg1', '288.v1', '432.bg1', '432.cg1', '432.fh1'], 'contains': ['1728.b1', '2592.bp1', '2592.bx1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [10909, 22752, 15552, 31084], 'label': '31104.fx.864.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bj1', 'old_label': '864.cb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cb1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246747
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '48.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1', '24.d1'], 'contains': ['96.a1', '96.b1', '96.d1', '96.s1', '96.bc1', '144.f1', '144.g1', '144.j1'], 'core': '576.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [1, 4032, 12096, 36, 12384, 15552, 10924], 'label': '31104.fx.48.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.d1', 'old_label': '48.a1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.a1', 'subgroup_fusion': None, 'weyl_group': '648.610'}
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id: 186246748
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.gh1', '288.w1', '432.bg1', '432.bu1', '432.gn1'], 'contains': ['1728.b1', '2592.bq1', '2592.by1', '2592.bz1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [505, 15552, 29068, 10368], 'label': '31104.fx.864.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.eb1', 'old_label': '864.cc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cc1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186246749
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.gi1', '288.x1', '432.fl1'], 'contains': ['1728.c1', '2592.bp1', '2592.ca1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [26029, 10368, 18144, 13852], 'label': '31104.fx.864.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.bv1', 'old_label': '864.cd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cd1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186246750
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ed1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.t1', '288.v1', '288.x1', '432.h1', '432.bo1', '432.ck1', '432.cq1', '432.cu1', '432.ed1', '432.ff1'], 'contains': ['1728.d1', '2592.bp1', '2592.br1', '2592.bs1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26029, 22752, 10368, 18144], 'label': '31104.fx.864.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cr1', 'old_label': '864.ce1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ce1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186246751
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.ea1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.u1', '288.w1', '432.bc1', '432.bo1', '432.bs1', '432.bt1', '432.ck1', '432.ef1', '432.gs1'], 'contains': ['1728.d1', '2592.bq1', '2592.bt1', '2592.bu1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [15625, 18144, 22752, 10368], 'label': '31104.fx.864.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bc1', 'old_label': '864.cf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cf1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
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id: 186246752
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.t1', '288.y1', '432.j1', '432.bp1', '432.cl1', '432.co1', '432.cs1', '432.eh1', '432.fo1'], 'contains': ['1728.e1', '2592.br1', '2592.bv1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [26461, 12384, 15552, 1728], 'label': '31104.fx.864.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bc1', 'old_label': '864.cg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cg1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246753
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.t1', '432.k1', '432.bq1', '432.cm1', '432.cp1', '432.ct1', '432.ei1', '432.fp1'], 'contains': ['1728.g1', '2592.bs1', '2592.bv1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [13069, 12384, 18144, 1728], 'label': '31104.fx.864.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bc1', 'old_label': '864.ch1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ch1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246754
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.u1', '288.z1', '288.ba1', '432.ba1', '432.bp1', '432.cb1', '432.ce1', '432.cl1', '432.ek1', '432.gl1'], 'contains': ['1728.e1', '2592.bt1', '2592.bw1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [16057, 1728, 15552, 12384], 'label': '31104.fx.864.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cu1', 'old_label': '864.ci1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ci1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186246755
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.u1', '432.bb1', '432.bq1', '432.cc1', '432.cf1', '432.cm1', '432.ek2', '432.gm1'], 'contains': ['1728.g1', '2592.bu1', '2592.bw1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [2665, 1728, 18144, 12384], 'label': '31104.fx.864.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ct1', 'old_label': '864.cj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cj1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246756
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.gp1', '288.v1', '432.bh1', '432.ch1', '432.fq1'], 'contains': ['1728.h1', '2592.bs1', '2592.bx1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [10909, 2016, 15552, 31084], 'label': '31104.fx.864.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bj1', 'old_label': '864.ck1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ck1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246757
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.gq1', '288.w1', '432.bh1', '432.bv1', '432.gt1'], 'contains': ['1728.h1', '2592.bu1', '2592.by1', '2592.bz1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [505, 15552, 29068, 2016], 'label': '31104.fx.864.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ef1', 'old_label': '864.cl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cl1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186246758
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '48.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1', '24.d1'], 'contains': ['96.a1', '96.e1', '96.f1', '144.h1', '144.i1', '144.k1'], 'core': '576.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [505, 4032, 12096, 36, 12384, 15552, 29068], 'label': '31104.fx.48.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.d1', 'old_label': '48.b1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.b1', 'subgroup_fusion': None, 'weyl_group': '648.610'}
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id: 186246759
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.gr1', '288.v1', '288.y1', '432.bi1', '432.ci1', '432.fr1'], 'contains': ['1728.i1', '2592.br1', '2592.bx1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [10909, 12384, 15552, 31084], 'label': '31104.fx.864.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bj1', 'old_label': '864.cm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cm1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246760
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.gs1', '288.w1', '288.z1', '432.bi1', '432.bw1', '432.gu1'], 'contains': ['1728.i1', '2592.bt1', '2592.by1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [505, 15552, 18700, 12384], 'label': '31104.fx.864.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bn1', 'old_label': '864.cn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cn1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
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id: 186246761
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.gt1', '288.w1', '288.ba1', '432.gz1'], 'contains': ['1728.j1', '2592.bt1', '2592.bz1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [505, 15552, 29068, 12384], 'label': '31104.fx.864.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.cp1', 'old_label': '864.co1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.co1', 'subgroup_fusion': None, 'weyl_group': '108.25'}
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id: 186246762
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.gu1', '288.x1', '288.y1', '432.fw1'], 'contains': ['1728.k1', '2592.br1', '2592.ca1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [26029, 2016, 18144, 13852], 'label': '31104.fx.864.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.bv1', 'old_label': '864.cp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cp1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186246763
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.gv1', '288.x1', '432.fx1'], 'contains': ['1728.m1', '2592.bs1', '2592.ca1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [26029, 12384, 18144, 13852], 'label': '31104.fx.864.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.bv1', 'old_label': '864.cq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cq1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186246764
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.bb1', '432.cv1', '432.da1', '432.db1', '432.de1', '432.dh1', '432.dj1', '432.dl1', '432.dq1', '432.dv1', '432.dy1', '432.dz1', '432.ea1', '432.eb1', '432.em1', '432.hk1'], 'contains': ['1728.a1', '1728.n1', '2592.cb1', '2592.cd1', '2592.cf1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [18144, 16056, 12096, 22752], 'label': '31104.fx.864.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '864.cr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cr1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186246765
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.bb1', '432.cw1', '432.dc1', '432.df1', '432.dm1', '432.dr1', '432.el1', '432.hk1'], 'contains': ['1728.a1', '1728.o1', '2592.cb1', '2592.ce1', '2592.cf1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [15552, 2592, 12096, 22752], 'label': '31104.fx.864.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.s1', 'old_label': '864.cs1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cs1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186246766
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.cm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.bb1', '432.cx1', '432.dd1', '432.dg1', '432.di1', '432.dn1', '432.ds1', '432.dx1', '432.ec1', '432.ed1', '432.ee1', '432.ef1', '432.en1', '432.hn1'], 'contains': ['1728.d1', '1728.p1', '2592.cb1', '2592.cc1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [18144, 16056, 22752, 10368], 'label': '31104.fx.864.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '864.ct1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ct1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186246767
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.bb1', '432.cy1', '432.dk1', '432.do1', '432.do2', '432.dt1', '432.dw1', '432.eg1', '432.eh1', '432.ei1', '432.ej1', '432.ek1', '432.ek2', '432.eo1', '432.ho1', '432.hq1'], 'contains': ['1728.e1', '1728.g1', '1728.q1', '2592.cc1', '2592.cd1', '2592.ce1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [18648, 72, 12096, 12384], 'label': '31104.fx.864.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '864.cu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cu1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186246768
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.bb1', '432.cz1', '432.dp1', '432.dp2', '432.du1', '432.ep1', '432.hp1', '432.hq1'], 'contains': ['1728.f1', '1728.g1', '1728.r1', '2592.cc1', '2592.ce1', '2592.cf1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [16056, 18144, 12096, 12384], 'label': '31104.fx.864.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1', 'old_label': '864.cv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cv1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186246769
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1', '24.d1'], 'contains': ['96.b1', '96.c1', '96.f1', '144.l1', '144.n1', '144.p1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [505, 4032, 12096, 18684, 12384, 15552, 29068], 'label': '31104.fx.48.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.d1', 'old_label': '48.c1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1', 'subgroup_fusion': None, 'weyl_group': '648.610'}
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id: 186246770
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.bc1', '288.bd1', '288.bi1', '432.fb1', '432.fg1', '432.gg1', '432.gk1', '432.hk1'], 'contains': ['1728.a1', '2592.cg1', '2592.cj1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [3096, 15552, 12096, 22752], 'label': '31104.fx.864.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1', 'old_label': '864.cw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cw1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186246771
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bj1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.gx1', '288.be1', '288.bf1', '288.bj1', '432.er1', '432.fh1', '432.gn1'], 'contains': ['1728.b1', '2592.cg1', '2592.ck1', '2592.cn1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [3096, 15552, 10924, 22752], 'label': '31104.fx.864.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1', 'old_label': '864.cx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cx1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186246772
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bk1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.be1', '288.bf1', '288.bk1', '432.es1', '432.fi1', '432.gd1', '432.go1', '432.hl1'], 'contains': ['2592.cg1', '2592.cl1', '2592.co1', '3456.c1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [28996, 22752, 72, 18144], 'label': '31104.fx.864.cy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '864.cy1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cy1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186246773
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.gy1', '288.be1', '288.bf1', '288.bl1', '432.et1', '432.fj1', '432.gp1'], 'contains': ['2592.cg1', '2592.cm1', '2592.cp1', '3456.d1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [5712, 22752, 18648, 15552], 'label': '31104.fx.864.cz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1', 'old_label': '864.cz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cz1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186246774
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.a1', '288.bc1', '288.bf1', '288.bg1', '288.bl1', '432.eu1', '432.fk1', '432.gq1'], 'contains': ['2592.cg1', '2592.cm1', '3456.e1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [5712, 10368, 18648, 15552], 'label': '31104.fx.864.da1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1', 'old_label': '864.da1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.da1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
-
id: 186246775
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.gz1', '288.bd1', '288.be1', '288.bh1', '288.bl1', '432.gr1'], 'contains': ['2592.cg1', '2592.cp1', '3456.f1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [28464, 10368, 18648, 15552], 'label': '31104.fx.864.db1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.c1', 'old_label': '864.db1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.db1', 'subgroup_fusion': None, 'weyl_group': '72.42'}
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id: 186246776
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bm1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ha1', '288.bg1', '288.bh1', '288.bm1', '432.fl1'], 'contains': ['1728.c1', '2592.cg1', '2592.cq1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [18216, 18144, 22132, 10368], 'label': '31104.fx.864.dc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.o1', 'old_label': '864.dc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dc1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186246777
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.df1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.bg1', '288.bh1', '288.bn1', '432.fm1', '432.hm1'], 'contains': ['2592.cg1', '2592.cr1', '3456.g1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [22132, 10368, 18648, 15552], 'label': '31104.fx.864.dd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.u1', 'old_label': '864.dd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dd1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
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id: 186246778
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.hb1', '288.bc1', '288.bd1', '288.bo1', '432.fn1'], 'contains': ['2592.cg1', '2592.cs1', '3456.h1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [10732, 22752, 18648, 15552], 'label': '31104.fx.864.de1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.k1', 'old_label': '864.de1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.de1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
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id: 186246779
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.de2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.hb2', '288.bg1', '288.bh1', '288.bo1', '432.fn2'], 'contains': ['2592.cg1', '2592.cs1', '3456.h2'], 'core': '10368.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [24268, 10368, 18648, 15552], 'label': '31104.fx.864.de2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.o1', 'old_label': '864.de2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.de2', 'subgroup_fusion': None, 'weyl_group': '72.43'}
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id: 186246780
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '6.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.c1', '3.a1'], 'contains': ['12.c1', '12.o1', '12.t1', '18.v1', '18.x1', '18.ba1', '18.bc1', '96.w1'], 'core': '12.c1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [10405, 18144, 16080, 10368, 15552, 12138, 12460, 18576, 16056, 22752], 'label': '31104.fx.6.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.j1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.j1', 'subgroup_fusion': None, 'weyl_group': '3456.di'}
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id: 186246781
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '48.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1', '24.d1'], 'contains': ['96.c1', '96.d1', '96.e1', '144.q1', '144.r1', '144.t1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [1, 4032, 12096, 18684, 12384, 15552, 10924], 'label': '31104.fx.48.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.d1', 'old_label': '48.d1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.d1', 'subgroup_fusion': None, 'weyl_group': '648.610'}
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id: 186246782
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.bi1', '288.bj1', '288.bk1', '288.bl1', '288.bm1', '288.bn1', '288.bo1', '432.fc1', '432.ff1', '432.gh1', '432.gs1', '432.hn1'], 'contains': ['1728.d1', '2592.cg1', '2592.ch1', '2592.ci1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [3096, 15552, 22752, 10368], 'label': '31104.fx.864.df1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '864.df1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.df1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186246783
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.bi1', '288.bp1', '288.br1', '432.fd1', '432.fo1', '432.gi1', '432.gl1', '432.hq1'], 'contains': ['1728.e1', '1728.f1', '2592.ch1', '2592.cj1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [3096, 18648, 12096, 12384], 'label': '31104.fx.864.dg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '864.dg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dg1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186246784
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.bi1', '288.bq1', '288.bs1', '432.fe1', '432.fp1', '432.gj1', '432.gj2', '432.gm1', '432.ho1', '432.hp1'], 'contains': ['1728.g1', '2592.ci1', '2592.cj1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [18216, 18144, 12096, 12384], 'label': '31104.fx.864.dh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '864.dh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dh1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186246785
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.hd1', '288.bj1', '288.bt1', '288.by1', '432.ev1', '432.fq1', '432.gt1'], 'contains': ['1728.h1', '2592.ci1', '2592.ck1', '2592.cn1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [3096, 15552, 10924, 2016], 'label': '31104.fx.864.di1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1', 'old_label': '864.di1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.di1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186246786
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.he1', '288.bj1', '288.bp1', '288.bu1', '288.bw1', '432.ew1', '432.fr1', '432.gu1'], 'contains': ['1728.i1', '2592.ch1', '2592.ck1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [3096, 15552, 556, 12384], 'label': '31104.fx.864.dj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1', 'old_label': '864.dj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dj1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246787
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.bk1', '288.bv1', '288.bw1', '432.ex1', '432.fs1', '432.ge1', '432.gv1', '432.hr1'], 'contains': ['2592.ch1', '2592.cl1', '2592.co1', '3456.j1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [28996, 2016, 72, 18144], 'label': '31104.fx.864.dk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '864.dk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dk1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186246788
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.bk1', '288.bq1', '288.bx1', '288.by1', '432.ey1', '432.ft1', '432.gf1', '432.gw1', '432.hs1'], 'contains': ['2592.ci1', '2592.cl1', '3456.k1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [18628, 12384, 72, 18144], 'label': '31104.fx.864.dl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '864.dl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dl1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186246789
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.hf1', '288.bl1', '288.bv1', '288.bw1', '432.ez1', '432.fu1', '432.gx1'], 'contains': ['2592.ch1', '2592.cm1', '2592.cp1', '3456.l1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [76, 12384, 18648, 15552], 'label': '31104.fx.864.dm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1', 'old_label': '864.dm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dm1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186246790
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.hf1', '288.bl1', '288.bt1', '288.by1', '432.fa1', '432.fv1', '432.gy1'], 'contains': ['2592.ci1', '2592.cm1', '2592.cp1', '3456.l1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [76, 12384, 72, 18144], 'label': '31104.fx.864.dn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1', 'old_label': '864.dn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dn1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186246791
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.hg1', '288.bj1', '288.br1', '288.bv1', '288.bz1', '432.gz1'], 'contains': ['1728.j1', '2592.ch1', '2592.cn1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [3096, 15552, 10924, 12384], 'label': '31104.fx.864.do1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.c1', 'old_label': '864.do1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.do1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
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id: 186246792
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '48.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1', '16.a1', '24.c1'], 'contains': ['96.l1', '144.bh1', '144.bi1', '144.bj1', '144.bl1', '144.bm1', '144.bn1', '192.b1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [36, 12384, 15552, 76, 10368, 5712, 18648], 'label': '31104.fx.48.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1', 'old_label': '48.e1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.e1', 'subgroup_fusion': None, 'weyl_group': '432.746'}
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id: 186246793
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.bk1', '288.bs1', '288.bt1', '288.ca1', '432.ha1', '432.ht1'], 'contains': ['2592.ci1', '2592.co1', '3456.m1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [28996, 12384, 72, 18144], 'label': '31104.fx.864.dp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.e1', 'old_label': '864.dp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dp1', 'subgroup_fusion': None, 'weyl_group': '72.42'}
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id: 186246794
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.hh1', '288.bm1', '288.bp1', '288.br1', '432.fw1'], 'contains': ['1728.k1', '1728.l1', '2592.ch1', '2592.cq1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [18216, 18144, 13780, 2016], 'label': '31104.fx.864.dq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.i1', 'old_label': '864.dq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dq1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 186246795
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.hh2', '288.bm1', '288.bx1', '288.ca1', '432.fx1'], 'contains': ['1728.m1', '2592.ci1', '2592.cq1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [18216, 18144, 24148, 12384], 'label': '31104.fx.864.dr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.m1', 'old_label': '864.dr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dr1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186246796
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.df1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.bn1', '288.bu1', '288.bz1', '432.fy1', '432.hw1'], 'contains': ['2592.ch1', '2592.cr1', '3456.n1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [24148, 12384, 18648, 15552], 'label': '31104.fx.864.ds1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1', 'old_label': '864.ds1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ds1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
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id: 186246797
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.df1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.bn1', '288.bq1', '288.bs1', '432.fz1', '432.hu1', '432.hv1'], 'contains': ['2592.ci1', '2592.cr1', '3456.n2'], 'core': '31104.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [26236, 2016, 18648, 15552], 'label': '31104.fx.864.dt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.q1', 'old_label': '864.dt1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dt1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
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id: 186246798
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.hi1', '288.bo1', '288.bu1', '288.bz1', '432.ga1'], 'contains': ['2592.ch1', '2592.cs1', '3456.o1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [364, 12384, 18648, 15552], 'label': '31104.fx.864.du1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.l1', 'old_label': '864.du1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.du1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
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id: 186246799
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.dv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.hi1', '288.bo1', '288.bx1', '288.ca1', '432.gb1'], 'contains': ['2592.ci1', '2592.cs1', '3456.o1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [364, 12384, 72, 18144], 'label': '31104.fx.864.dv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.m1', 'old_label': '864.dv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dv1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
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id: 186246800
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.hj1', '288.be1', '288.bf1', '288.bt1', '288.bw1', '432.hb1'], 'contains': ['2592.ck1', '2592.cm1', '2592.co1', '2592.cp1', '3456.p1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [12460, 28464, 18648, 15552], 'label': '31104.fx.864.dw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.t1', 'old_label': '864.dw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dw1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186246801
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.dx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.hk1', '288.be1', '288.bt1', '288.bw1', '432.hc1'], 'contains': ['2592.ck1', '2592.co1', '2592.cp1', '3456.q1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [2524, 28464, 72, 18144], 'label': '31104.fx.864.dx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.t1', 'old_label': '864.dx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dx1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186246802
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.hj1', '288.be1', '288.bf1', '288.bv1', '288.by1', '432.hd1'], 'contains': ['2592.cl1', '2592.cm1', '2592.cn1', '2592.cp1', '3456.p1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [12892, 28464, 72, 18144], 'label': '31104.fx.864.dy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.t1', 'old_label': '864.dy1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dy1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186246803
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '48.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1', '16.a1', '24.d1'], 'contains': ['96.a1', '96.c1', '96.g1', '144.bl1', '144.bo1', '144.bq1'], 'core': '576.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [36, 2016, 12096, 3096, 10368, 15552, 10924], 'label': '31104.fx.48.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1', 'old_label': '48.f1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.f1', 'subgroup_fusion': None, 'weyl_group': '972.456'}
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id: 186246804
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.hk1', '288.be1', '288.bv1', '288.by1', '432.he1'], 'contains': ['2592.cl1', '2592.cn1', '2592.cp1', '3456.q1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [2092, 28464, 18648, 15552], 'label': '31104.fx.864.dz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.t1', 'old_label': '864.dz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dz1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186246805
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.hl1', '288.bf1', '288.bw1', '288.by1', '432.eq1', '432.gc1', '432.hf1'], 'contains': ['2592.ck1', '2592.cl1', '2592.cm1', '3456.r1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [20812, 5712, 18648, 15552], 'label': '31104.fx.864.ea1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1', 'old_label': '864.ea1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ea1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186246806
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.eb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.hm1', '288.be1', '288.bw1', '288.by1', '432.hg1'], 'contains': ['2592.ck1', '2592.cl1', '2592.cp1', '3456.s1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [76, 28464, 18648, 15552], 'label': '31104.fx.864.eb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.t1', 'old_label': '864.eb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.eb1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186246807
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.ec1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.hn1', '288.be1', '288.bf1', '288.bt1', '288.bv1', '432.hh1'], 'contains': ['2592.cm1', '2592.cn1', '2592.co1', '2592.cp1', '3456.t1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [76, 5712, 18648, 15552], 'label': '31104.fx.864.ec1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.t1', 'old_label': '864.ec1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ec1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186246808
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.ed1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.ho1', '288.bf1', '288.bt1', '288.bv1', '432.hi1'], 'contains': ['2592.cm1', '2592.cn1', '2592.co1', '3456.u1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [12460, 5712, 18648, 15552], 'label': '31104.fx.864.ed1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.t1', 'old_label': '864.ed1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ed1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186246809
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.ee1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.hp1', '288.be1', '288.bt1', '288.bv1', '432.hj2'], 'contains': ['2592.cn1', '2592.co1', '2592.cp1', '3456.v1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [10444, 28464, 18648, 15552], 'label': '31104.fx.864.ee1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.t1', 'old_label': '864.ee1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ee1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186246810
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.ee2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.hp2', '288.be1', '288.bt1', '288.bv1', '432.hj1'], 'contains': ['2592.cn1', '2592.co1', '2592.cp1', '3456.v2'], 'core': '31104.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [23260, 28464, 72, 18144], 'label': '31104.fx.864.ee2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.t1', 'old_label': '864.ee2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ee2', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186246811
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.ef1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.cb1', '432.a1', '432.cv1', '432.hx1', '432.hy1', '432.ic1', '432.ie1', '432.if1', '432.ih1', '432.ly1', '432.lz1'], 'contains': ['1728.n1', '1728.z1', '1728.cx2', '2592.ct1', '2592.cv1', '2592.cw1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [36, 18576, 12096, 10368], 'label': '31104.fx.864.ef1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '864.ef1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ef1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246812
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.eg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.cb1', '432.a1', '432.b1', '432.cw1', '432.hz1', '432.ig1', '432.ly1', '432.ma1'], 'contains': ['1728.o1', '1728.z1', '1728.cx1', '2592.ct1', '2592.cw1', '2592.cx1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [36, 16056, 12096, 10368], 'label': '31104.fx.864.eg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bb1', 'old_label': '864.eg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.eg1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246813
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.eh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.bd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.cb1', '432.c1', '432.cx1', '432.ia1', '432.ib1', '432.ii1', '432.ij1', '432.mb1'], 'contains': ['1728.p1', '1728.ba1', '1728.cy1', '2592.ct1', '2592.cu1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [36, 16056, 22752, 10368], 'label': '31104.fx.864.eh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '864.eh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.eh1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246814
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '24.e1', '24.h1'], 'contains': ['96.h1', '144.bm1', '144.bp1', '144.bq1', '192.c1'], 'core': '576.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [36, 2016, 12096, 10924, 10368, 72, 18144], 'label': '31104.fx.48.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '48.g1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.g1', 'subgroup_fusion': None, 'weyl_group': None}
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id: 186246815
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.ei1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.cb1', '432.d1', '432.f1', '432.cy1', '432.id1', '432.ik1', '432.mc1'], 'contains': ['1728.q1', '1728.bb1', '1728.cz1', '2592.cu1', '2592.cv1', '2592.cx1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [36, 18576, 12096, 12384], 'label': '31104.fx.864.ei1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '864.ei1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ei1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246816
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.cb1', '432.d1', '432.e1', '432.g1', '432.cz1', '432.mc1'], 'contains': ['1728.r1', '1728.bb1', '1728.cz2', '2592.cu1', '2592.cw1', '2592.cx1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [36, 16056, 12096, 12384], 'label': '31104.fx.864.ej1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.dw1', 'old_label': '864.ej1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ej1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 186246817
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.me1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.cc1', '432.da1', '432.hx1', '432.il1', '432.im1', '432.in1', '432.io1', '432.ip1', '432.iq1', '432.ir1', '432.is1', '432.it1', '432.jp1', '432.jq1', '432.md1', '432.me1'], 'contains': ['1728.n1', '1728.bc1', '2592.cy1', '2592.cz1', '2592.da1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [17371, 18576, 12096, 10368], 'label': '31104.fx.864.ek1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '864.ek1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ek1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186246818
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.el1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.mh1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.cc1', '432.db1', '432.hy1', '432.iv1', '432.iz1', '432.ja1', '432.jc1', '432.jd1', '432.jg1', '432.jj1', '432.jl1', '432.jm1', '432.jp1', '432.jq1', '432.mh1', '432.ml1'], 'contains': ['1728.n1', '1728.bf1', '2592.cz1', '2592.db1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [17371, 18576, 12096, 22752], 'label': '31104.fx.864.el1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '864.el1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.el1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246819
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.em1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.gc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.cc1', '432.dc1', '432.hz1', '432.iw1', '432.je1', '432.jh1', '432.mi1', '432.ml1'], 'contains': ['1728.o1', '1728.bf1', '2592.da1', '2592.db1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [12138, 16056, 12096, 10368], 'label': '31104.fx.864.em1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.g1', 'old_label': '864.em1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.em1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246820
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.en1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.nh1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.cc1', '432.dd1', '432.ia1', '432.iu1', '432.ix1', '432.iy1', '432.jb1', '432.jf1', '432.ji1', '432.jk1', '432.jn1', '432.jo1', '432.jr1', '432.js1', '432.mk1', '432.mo1'], 'contains': ['1728.p1', '1728.bj1', '2592.cy1', '2592.db1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [12138, 16056, 22752, 10368], 'label': '31104.fx.864.en1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '864.en1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.en1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246821
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.eo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.ka1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.cd1', '432.de1', '432.hy1', '432.il1', '432.im1', '432.iv1', '432.ju1', '432.jv1', '432.jy1', '432.kb1', '432.kd1', '432.ke1', '432.kp1', '432.kq1', '432.mr1', '432.mx1'], 'contains': ['1728.n1', '1728.bo1', '2592.dc1', '2592.de1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26047, 18576, 22752, 12096], 'label': '31104.fx.864.eo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '864.eo1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.eo1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246822
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.ep1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ep1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.cd1', '432.df1', '432.hz1', '432.iw1', '432.jw1', '432.jz1', '432.ms1', '432.mx1'], 'contains': ['1728.o1', '1728.bo1', '2592.dc1', '2592.df1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [26047, 2592, 22752, 12096], 'label': '31104.fx.864.ep1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.k1', 'old_label': '864.ep1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ep1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246823
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.eq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.kw1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.cd1', '432.dg1', '432.ia1', '432.iu1', '432.ix1', '432.iy1', '432.jt1', '432.jx1', '432.ka1', '432.kc1', '432.kf1', '432.kg1', '432.kh1', '432.ki1', '432.mw1', '432.na1'], 'contains': ['1728.p1', '1728.bu1', '2592.dc1', '2592.dd1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [6, 16056, 10368, 22752], 'label': '31104.fx.864.eq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '864.eq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.eq1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246843
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.fe1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.cg1', '432.v1', '432.w1', '432.y1', '432.cz1', '432.ns2'], 'contains': ['1728.r1', '1728.cw2', '1728.cw3', '2592.dp1', '2592.dr1', '2592.ds1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [18180, 16056, 12096, 12384], 'label': '31104.fx.864.fe1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.dw1', 'old_label': '864.fe1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fe1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 186246824
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.er1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.kj1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.cd1', '432.dh1', '432.hx1', '432.in1', '432.iz1', '432.ja1', '432.kj1', '432.kk1', '432.kl1', '432.km1', '432.kn1', '432.ko1', '432.kp1', '432.kq1', '432.nb1', '432.ne1'], 'contains': ['1728.n1', '1728.ca1', '2592.dd1', '2592.de1', '2592.df1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [6, 16056, 12096, 22752], 'label': '31104.fx.864.er1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '864.er1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.er1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186246825
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '48.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.a1', '16.a1', '24.f1'], 'contains': ['96.i1', '144.bk1', '144.bn1', '144.bq1', '192.d1'], 'core': '576.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [36, 12384, 12096, 76, 10368, 18648, 15552], 'label': '31104.fx.48.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1', 'old_label': '48.h1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.h1', 'subgroup_fusion': None, 'weyl_group': None}
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id: 186246826
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.es1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.di1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.ce1', '432.di1', '432.ib1', '432.iu1', '432.jb1', '432.jt1', '432.kr1', '432.ks1', '432.kt1', '432.nf1'], 'contains': ['1728.p1', '1728.cd1', '2592.dg1', '2592.dh1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [10405, 2592, 22752, 10368], 'label': '31104.fx.864.es1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '864.es1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.es1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186246827
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.et1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.dd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.ce1', '432.dj1', '432.ic1', '432.il1', '432.io1', '432.iz1', '432.jc1', '432.ju1', '432.kj1', '432.ku1', '432.kw1', '432.kw2', '432.ky1', '432.kz1', '432.ng1', '432.nh1'], 'contains': ['1728.n1', '1728.ce1', '2592.dg1', '2592.di1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [10405, 2592, 10368, 1728], 'label': '31104.fx.864.et1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '864.et1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.et1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246828
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.eu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.ce1', '432.dk1', '432.id1', '432.kv1', '432.kx1', '432.nl1'], 'contains': ['1728.q1', '1728.ck1', '2592.dh1', '2592.di1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [10405, 2592, 12384, 1728], 'label': '31104.fx.864.eu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.h1', 'old_label': '864.eu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.eu1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246829
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.ev1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.cf1', '432.a1', '432.l1', '432.l2', '432.s1', '432.dl1', '432.no1', '432.np1'], 'contains': ['1728.n1', '1728.cu1', '1728.cx1', '2592.dj1', '2592.dl1', '2592.dm1', '2592.dm2'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [15588, 16056, 12096, 22752], 'label': '31104.fx.864.ev1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.du1', 'old_label': '864.ev1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ev1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 186246830
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.ew1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.cf1', '432.a1', '432.l2', '432.m1', '432.t1', '432.dm1', '432.no2', '432.nq1'], 'contains': ['1728.o1', '1728.cu1', '1728.cx2', '2592.dj1', '2592.dm1', '2592.dn1', '2592.dn2'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [2628, 16056, 12096, 10368], 'label': '31104.fx.864.ew1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.du1', 'old_label': '864.ew1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ew1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 186246831
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.ew2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.cf1', '432.b1', '432.l1', '432.m1', '432.s1', '432.dm1', '432.no1', '432.nq1'], 'contains': ['1728.o1', '1728.cu1', '1728.cx1', '2592.dj1', '2592.dm2', '2592.dn1', '2592.dn3'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [15588, 432, 12096, 22752], 'label': '31104.fx.864.ew2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.du1', 'old_label': '864.ew2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ew2', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 186246832
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.ex1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.cf1', '432.c1', '432.n1', '432.u1', '432.dn1', '432.nr1'], 'contains': ['1728.p1', '1728.cv1', '1728.cy1', '2592.dj1', '2592.dk1', '2592.dk2'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [15588, 16056, 22752, 10368], 'label': '31104.fx.864.ex1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.dv1', 'old_label': '864.ex1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ex1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 186246833
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.ey1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.cf1', '432.d1', '432.q1', '432.v1', '432.do2', '432.ns2'], 'contains': ['1728.q1', '1728.cw2', '1728.cz2', '2592.dk1', '2592.dl1', '2592.dn1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [15588, 18576, 12096, 12384], 'label': '31104.fx.864.ey1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.dw1', 'old_label': '864.ey1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ey1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 186246834
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.ey2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.cf1', '432.f1', '432.o1', '432.x1', '432.do1', '432.ns2'], 'contains': ['1728.q1', '1728.cw3', '1728.cz1', '2592.dk2', '2592.dl1', '2592.dn2', '2592.dn3'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [18252, 18576, 12096, 12384], 'label': '31104.fx.864.ey2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.dw1', 'old_label': '864.ey2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ey2', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 186246835
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.ez1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.cf1', '432.d1', '432.r2', '432.w1', '432.dp2', '432.ns2'], 'contains': ['1728.r1', '1728.cw2', '1728.cz1', '2592.dk1', '2592.dm2', '2592.dn2'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [540, 16056, 12096, 12384], 'label': '31104.fx.864.ez1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.dw1', 'old_label': '864.ez1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ez1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 186246836
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '48.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1', '16.b1', '24.d1'], 'contains': ['96.b1', '96.e1', '96.g1', '144.br1', '144.bs1', '144.bv1', '144.cb1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [10405, 1728, 12940, 3096, 12384, 10368, 15552], 'label': '31104.fx.48.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.d1', 'old_label': '48.i1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.i1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186246837
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.ez2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.cf1', '432.e1', '432.r1', '432.v1', '432.dp2', '432.ns1'], 'contains': ['1728.r1', '1728.cw1', '1728.cz2', '2592.dk1', '2592.dm1', '2592.dn3'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [18684, 16056, 12096, 12384], 'label': '31104.fx.864.ez2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.dw1', 'old_label': '864.ez2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ez2', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 186246838
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.ez3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.cf1', '432.g1', '432.o1', '432.p1', '432.y1', '432.dp1', '432.ns1', '432.ns2'], 'contains': ['1728.r1', '1728.cw3', '1728.cz2', '2592.dk2', '2592.dm1', '2592.dm2', '2592.dn1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [108, 16056, 12096, 12384], 'label': '31104.fx.864.ez3', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.dw1', 'old_label': '864.ez3', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ez3', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 186246839
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.fa1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.cg1', '432.s1', '432.cv1', '432.ip1', '432.jd1', '432.jv1', '432.kk1', '432.ku1', '432.la1', '432.no2', '432.np1'], 'contains': ['1728.n1', '1728.cu1', '2592.do1', '2592.dq1', '2592.dr1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [18684, 18576, 12096, 10368], 'label': '31104.fx.864.fa1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '864.fa1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fa1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186246840
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.fb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.cg1', '432.s1', '432.t1', '432.cw1', '432.je1', '432.jw1', '432.no1', '432.nq1'], 'contains': ['1728.o1', '1728.cu1', '2592.do1', '2592.dr1', '2592.ds1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [18180, 16056, 12096, 10368], 'label': '31104.fx.864.fb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bb1', 'old_label': '864.fb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fb1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246841
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.fc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.bd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.cg1', '432.u1', '432.cx1', '432.jf1', '432.jx1', '432.kr1', '432.lb1', '432.nr1'], 'contains': ['1728.p1', '1728.cv1', '2592.do1', '2592.dp1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [18180, 16056, 22752, 10368], 'label': '31104.fx.864.fc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '864.fc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fc1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246842
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.fd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.cg1', '432.v1', '432.x1', '432.cy1', '432.kv1', '432.lc1', '432.ns1'], 'contains': ['1728.q1', '1728.cw1', '1728.cw3', '2592.dp1', '2592.dq1', '2592.ds1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [108, 18576, 12096, 12384], 'label': '31104.fx.864.fd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '864.fd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fd1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246844
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.ff1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.ch1', '432.l1', '432.dq1', '432.iq1', '432.iv1', '432.kl1', '432.kw2', '432.ld2', '432.lh1', '432.ly1', '432.np1'], 'contains': ['1728.n1', '1728.cx1', '2592.dt1', '2592.dv1', '2592.dw1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [468, 16056, 12096, 22752], 'label': '31104.fx.864.ff1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '864.ff1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ff1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186246845
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.ff2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.ch1', '432.l2', '432.dq1', '432.in1', '432.jg1', '432.jy1', '432.kw1', '432.ld1', '432.lg1', '432.lz1', '432.no2'], 'contains': ['1728.n1', '1728.cx2', '2592.dt2', '2592.dv1', '2592.dw2'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [18612, 16056, 12096, 22752], 'label': '31104.fx.864.ff2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '864.ff2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ff2', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246846
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.fg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.ch1', '432.l1', '432.m1', '432.dr1', '432.jh1', '432.jz1', '432.ma1', '432.no1'], 'contains': ['1728.o1', '1728.cx1', '2592.dt2', '2592.dw1', '2592.dx1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [468, 16056, 12096, 10368], 'label': '31104.fx.864.fg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bb1', 'old_label': '864.fg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fg1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246847
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '48.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1', '24.e1', '24.g1', '24.i1'], 'contains': ['96.h1', '144.br1', '144.bt1', '144.bw1', '144.cc1', '192.m1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [10405, 72, 12384, 10368, 18144, 12940, 1728], 'label': '31104.fx.48.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1', 'old_label': '48.j1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.j1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186246848
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.fg2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.ch1', '432.l2', '432.m1', '432.dr1', '432.iw1', '432.li1', '432.ly1', '432.nq1'], 'contains': ['1728.o1', '1728.cx1', '1728.cx2', '2592.dt1', '2592.dw2', '2592.dx1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [18612, 16056, 12096, 10368], 'label': '31104.fx.864.fg2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bb1', 'old_label': '864.fg2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fg2', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246849
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.fh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.ch1', '432.n1', '432.ds1', '432.ix1', '432.ji1', '432.ka1', '432.ks1', '432.lf1', '432.lj1', '432.mb1', '432.nr1'], 'contains': ['1728.p1', '1728.cy1', '2592.dt1', '2592.dt2', '2592.du1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [468, 16056, 22752, 10368], 'label': '31104.fx.864.fh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '864.fh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fh1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186246850
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.fi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.ch1', '432.o1', '432.q1', '432.dt1', '432.kx1', '432.le1', '432.mc1', '432.ns1'], 'contains': ['1728.q1', '1728.cz2', '2592.du1', '2592.dv1', '2592.dx1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [2628, 18576, 12096, 12384], 'label': '31104.fx.864.fi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '864.fi1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fi1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246851
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.fj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.ch1', '432.o1', '432.p1', '432.r1', '432.r2', '432.du1', '432.mc1', '432.ns2'], 'contains': ['1728.r1', '1728.cz1', '1728.cz2', '2592.du1', '2592.dw1', '2592.dw2', '2592.dx1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [468, 16056, 12096, 12384], 'label': '31104.fx.864.fj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.dw1', 'old_label': '864.fj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fj1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 186246852
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.fk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.ct1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.ci1', '432.dv1', '432.ic1', '432.ir1', '432.jj1', '432.jp1', '432.kb1', '432.km1', '432.kp1', '432.ku1', '432.ld1', '432.ld2', '432.lk1', '432.ll1', '432.nt1', '432.nu1'], 'contains': ['1728.n1', '1728.da1', '2592.dy1', '2592.dz1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1, 2592, 1728, 10368], 'label': '31104.fx.864.fk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '864.fk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fk1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186246853
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.fl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.ci1', '432.dw1', '432.id1', '432.kv1', '432.le1', '432.nv1'], 'contains': ['1728.q1', '1728.db1', '2592.dy1', '2592.ea1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1, 2592, 1728, 12384], 'label': '31104.fx.864.fl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.p1', 'old_label': '864.fl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fl1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246854
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.fm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.dc1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.ci1', '432.dx1', '432.ib1', '432.jk1', '432.jr1', '432.kc1', '432.kh1', '432.kr1', '432.lf1', '432.lm1', '432.ln1', '432.nz1'], 'contains': ['1728.p1', '1728.dg1', '2592.dz1', '2592.ea1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1, 2592, 22752, 10368], 'label': '31104.fx.864.fm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '864.fm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fm1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186246855
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.fn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ob1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.cj1', '432.da1', '432.ie1', '432.jj1', '432.jl1', '432.ju1', '432.kd1', '432.kk1', '432.kl1', '432.ky1', '432.lg1', '432.lk1', '432.lo1', '432.lq1', '432.md1', '432.ob1'], 'contains': ['1728.n1', '2592.eb1', '2592.ej1', '2592.ek1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [2179, 12096, 10368, 18576], 'label': '31104.fx.864.fn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '864.fn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fn1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186246856
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.fo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.mh1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.cj1', '432.db1', '432.if1', '432.ir1', '432.is1', '432.jv1', '432.jy1', '432.kj1', '432.kn1', '432.kz1', '432.lh1', '432.lk1', '432.lp1', '432.lq1', '432.mh1', '432.oc1'], 'contains': ['1728.n1', '2592.ec1', '2592.ej1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [19891, 12096, 18576, 22752], 'label': '31104.fx.864.fo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '864.fo1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fo1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246857
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.fp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.gc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.cj1', '432.dc1', '432.ig1', '432.jw1', '432.jz1', '432.li1', '432.mi1', '432.od1'], 'contains': ['1728.o1', '2592.ec1', '2592.ek1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [30282, 12096, 16056, 10368], 'label': '31104.fx.864.fp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.g1', 'old_label': '864.fp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fp1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246858
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '48.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.r1', '16.b1', '24.f1'], 'contains': ['96.i1', '144.br1', '144.bu1', '144.bx1', '144.by1', '192.n1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [10405, 18648, 10368, 22752, 15552, 16080, 1728], 'label': '31104.fx.48.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '48.k1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.k1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186246859
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.fq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.dd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.ck1', '432.dy1', '432.ih1', '432.im1', '432.it1', '432.ja1', '432.jm1', '432.kd1', '432.kn1', '432.la1', '432.ld1', '432.ld2', '432.lo1', '432.lp1', '432.ng1', '432.nh1'], 'contains': ['1728.n1', '2592.ed1', '2592.el1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [26389, 10368, 2592, 1728], 'label': '31104.fx.864.fq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '864.fq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fq1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246860
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.fr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.ka1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.cl1', '432.de1', '432.if1', '432.io1', '432.it1', '432.jd1', '432.jg1', '432.km1', '432.ko1', '432.ky1', '432.lh1', '432.ll1', '432.lo1', '432.lr1', '432.mr1', '432.oe2'], 'contains': ['1728.n1', '2592.ee1', '2592.em1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [28567, 22752, 18576, 12096], 'label': '31104.fx.864.fr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '864.fr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fr1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246861
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.fs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ep1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.cl1', '432.df1', '432.ig1', '432.je1', '432.jh1', '432.li1', '432.ms1', '432.oe1'], 'contains': ['1728.o1', '2592.ee1', '2592.en1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [10495, 22752, 2592, 12096], 'label': '31104.fx.864.fs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.k1', 'old_label': '864.fs1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fs1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246862
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.ft1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.ll1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.cl1', '432.dh1', '432.ie1', '432.ip1', '432.iq1', '432.jc1', '432.jm1', '432.kb1', '432.ke1', '432.kz1', '432.lg1', '432.ll1', '432.lp1', '432.lr1', '432.nb1', '432.of1'], 'contains': ['1728.n1', '2592.ef1', '2592.em1', '2592.en1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [10855, 18576, 12096, 10368], 'label': '31104.fx.864.ft1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '864.ft1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ft1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186246863
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.fu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.ct1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.cm1', '432.ea1', '432.ih1', '432.is1', '432.jl1', '432.jq1', '432.ke1', '432.ko1', '432.kq1', '432.kw1', '432.kw2', '432.la1', '432.lq1', '432.lr1', '432.nt1', '432.nu1'], 'contains': ['1728.n1', '2592.eg1', '2592.eo1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [15985, 1728, 2592, 10368], 'label': '31104.fx.864.fu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '864.fu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fu1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246864
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.fv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.nh1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.cj1', '432.dd1', '432.ii1', '432.jk1', '432.jn1', '432.jt1', '432.jx1', '432.ka1', '432.kf1', '432.kt1', '432.lj1', '432.lm1', '432.ls1', '432.lt1', '432.mk1', '432.og1'], 'contains': ['1728.p1', '2592.eb1', '2592.ec1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [30282, 22752, 16056, 10368], 'label': '31104.fx.864.fv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '864.fv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fv1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246865
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.fw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ec1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.ck1', '432.ec1', '432.ij1', '432.iy1', '432.jo1', '432.kf1', '432.lb1', '432.lf1', '432.ls1', '432.nf1'], 'contains': ['1728.p1', '2592.ed1', '2592.eh1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [26389, 22752, 10368, 2592], 'label': '31104.fx.864.fw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '864.fw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fw1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186246866
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.fx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.kw1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.cl1', '432.dg1', '432.ii1', '432.jb1', '432.jf1', '432.ji1', '432.jo1', '432.kc1', '432.kg1', '432.kt1', '432.lj1', '432.ln1', '432.ls1', '432.lu1', '432.mw1', '432.oh1'], 'contains': ['1728.p1', '2592.ee1', '2592.ef1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [10855, 22752, 18576, 10368], 'label': '31104.fx.864.fx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '864.fx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fx1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246867
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.fy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.dz1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.cm1', '432.ee1', '432.ij1', '432.jn1', '432.js1', '432.kg1', '432.ki1', '432.ks1', '432.lb1', '432.lt1', '432.lu1', '432.nz1'], 'contains': ['1728.p1', '2592.eg1', '2592.ei1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [15985, 2592, 22752, 10368], 'label': '31104.fx.864.fy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '864.fy1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fy1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186246868
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.fz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.ck1', '432.eg1', '432.ik1', '432.lc1', '432.le1', '432.nl1'], 'contains': ['1728.q1', '2592.eh1', '2592.el1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [28981, 12384, 2592, 1728], 'label': '31104.fx.864.fz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.h1', 'old_label': '864.fz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fz1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246869
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '48.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.s1', '16.b1'], 'contains': ['96.j1', '144.bs1', '144.bw1', '144.bx1', '144.cd1', '192.o1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [10405, 18648, 12384, 10368, 15552, 24268, 9168], 'label': '31104.fx.48.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.l1', 'old_label': '48.l1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.l1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
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id: 186246870
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.ga1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.cm1', '432.ej1', '432.ik1', '432.kx1', '432.lc1', '432.nv1'], 'contains': ['1728.q1', '2592.ei1', '2592.eo1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [18577, 1728, 2592, 12384], 'label': '31104.fx.864.ga1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.p1', 'old_label': '864.ga1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ga1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246871
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.gb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.cr1', '432.el1', '432.em1', '432.ly1', '432.md1', '432.ml1', '432.mx1', '432.nb1', '432.ng1', '432.no1', '432.no2', '432.nt1', '432.oc1', '432.od1', '432.oe1', '432.oe2'], 'contains': ['1728.n1', '1728.o1', '2592.ep1', '2592.er1', '2592.es1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [432, 16056, 12096, 22752], 'label': '31104.fx.864.gb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '864.gb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gb1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 186246872
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.gc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.bs1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.cn1', '288.cp1', '288.cr1', '432.em1', '432.lz1', '432.me1', '432.mh1', '432.mr1', '432.ne1', '432.nh1', '432.np1', '432.nu1', '432.ob1', '432.of1'], 'contains': ['1728.n1', '2592.ep2', '2592.er1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [16056, 18576, 12096, 22752], 'label': '31104.fx.864.gc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '864.gc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gc1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186246873
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.gd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.co1', '288.cq1', '288.cr1', '432.el1', '432.ma1', '432.mi1', '432.ms1', '432.nq1'], 'contains': ['1728.o1', '2592.ep2', '2592.es1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [16056, 432, 12096, 10368], 'label': '31104.fx.864.gd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '864.gd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gd1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186246874
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.ge1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.bu1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.gy1', '288.cs1', '432.lv1', '432.mj1', '432.mm1', '432.mq1', '432.nc1', '432.ni1', '432.nw1'], 'contains': ['2592.ep1', '2592.et1', '2592.eu1', '3456.d1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [20760, 22752, 15624, 432], 'label': '31104.fx.864.ge1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.dj1', 'old_label': '864.ge1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ge1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186246875
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.gf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.bj1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.a1', '288.cn1', '288.co1', '288.cs1', '432.lw1', '432.mf1', '432.mp1', '432.mt1', '432.my1', '432.nj1', '432.nx1'], 'contains': ['2592.ep2', '2592.et1', '3456.e1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [20812, 22752, 2664, 18576], 'label': '31104.fx.864.gf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.x1', 'old_label': '864.gf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gf1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186246876
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.gg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.gz1', '288.cp1', '288.cq1', '288.cs1', '432.mu1', '432.mz1', '432.ny1'], 'contains': ['2592.ep2', '2592.eu1', '3456.f1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [12408, 10368, 15624, 432], 'label': '31104.fx.864.gg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.w1', 'old_label': '864.gg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gg1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186246877
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.gh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.bj1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.hb1', '288.cn1', '288.cq1', '288.ct1', '432.mg1', '432.mv1', '432.nk1'], 'contains': ['2592.ep2', '2592.ev1', '3456.h1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [10732, 22752, 432, 2592], 'label': '31104.fx.864.gh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.t1', 'old_label': '864.gh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gh1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
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id: 186246878
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.gh2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.hb1', '288.co1', '288.cp1', '288.cq1', '288.ct1', '432.mv2'], 'contains': ['2592.ep2', '2592.ev2', '3456.h1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [29308, 22752, 2664, 18576], 'label': '31104.fx.864.gh2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.z1', 'old_label': '864.gh2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gh2', 'subgroup_fusion': None, 'weyl_group': '72.43'}
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id: 186246879
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.gh3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.hb2', '288.ct1', '432.mn1', '432.nd1', '432.nk2'], 'contains': ['2592.ep1', '2592.ev1', '2592.ev2', '3456.h2'], 'core': '10368.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [24268, 10368, 2664, 18576], 'label': '31104.fx.864.gh3', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.es1', 'old_label': '864.gh3', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gh3', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186246880
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '48.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.s1', '16.b1'], 'contains': ['96.k1', '144.bt1', '144.bv1', '144.bx1', '144.cf1', '192.o1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [10405, 18216, 12384, 10368, 18144, 24700, 9168], 'label': '31104.fx.48.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.m1', 'old_label': '48.m1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.m1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
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id: 186246881
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.gi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.cr1', '288.cs1', '288.ct1', '432.en1', '432.mb1', '432.mk1', '432.mo1', '432.mw1', '432.na1', '432.nf1', '432.nr1', '432.nz1', '432.og1', '432.oh1'], 'contains': ['1728.p1', '2592.ep1', '2592.ep2', '2592.eq1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [16056, 18576, 10368, 22752], 'label': '31104.fx.864.gi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '864.gi1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gi1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246882
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.gj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.cr1', '432.eo1', '432.ep1', '432.mc1', '432.nl1', '432.ns1', '432.ns2', '432.nv1'], 'contains': ['1728.q1', '1728.r1', '2592.eq1', '2592.er1', '2592.es1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [16056, 432, 12096, 12384], 'label': '31104.fx.864.gj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '864.gj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gj1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186246883
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.gk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.hf1', '288.cs1', '432.lx1', '432.nm1', '432.oa1'], 'contains': ['2592.eq1', '2592.et1', '2592.eu1', '3456.l1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [76, 12384, 2664, 18576], 'label': '31104.fx.864.gk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.ef1', 'old_label': '864.gk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gk1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186246884
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.gl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.hi1', '288.ct1', '432.nn1'], 'contains': ['2592.eq1', '2592.ev1', '2592.ev2', '3456.o1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [29904, 17520, 15624, 432], 'label': '31104.fx.864.gl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fo1', 'old_label': '864.gl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gl1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186246885
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.gm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.p1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.o1', '288.cu1', '288.cv1', '432.oi1'], 'contains': ['1728.s1', '1728.bk1', '1728.bv1', '2592.ew1', '2592.ex1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [19135, 36, 18672, 15484], 'label': '31104.fx.864.gm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.oi1', 'old_label': '864.gm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gm1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186246886
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.gn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.ea1', '288.cw1', '288.cx1', '432.oi1'], 'contains': ['1728.s1', '1728.cq1', '1728.dn1', '2592.ey1', '2592.ez1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [20737, 36, 30964, 16080], 'label': '31104.fx.864.gn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.oi1', 'old_label': '864.gn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gn1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246887
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.go1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.v1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.jq1', '288.cu1', '288.cy1', '288.cz1', '432.ok1'], 'contains': ['1728.v1', '1728.bd1', '1728.bq1', '2592.ew1', '2592.fa1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [29503, 36, 16080, 10368], 'label': '31104.fx.864.go1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.ok1', 'old_label': '864.go1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.go1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186246888
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.gp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.ba1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.js1', '288.cv1', '288.cz1', '432.oj1'], 'contains': ['1728.u1', '1728.bh1', '1728.bn1', '2592.ew1', '2592.fc1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [19135, 36, 16080, 22752], 'label': '31104.fx.864.gp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.oj1', 'old_label': '864.gp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gp1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186246889
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.gq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.be1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.jr1', '288.cu1', '288.db1', '432.oj1'], 'contains': ['1728.u1', '1728.bg1', '1728.cb1', '2592.ex1', '2592.fa1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [24198, 36, 16080, 22752], 'label': '31104.fx.864.gq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fx1', 'old_label': '864.gq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gq1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246890
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.gr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.jt1', '288.cv1', '288.da1', '288.db1', '432.ok1'], 'contains': ['1728.v1', '1728.bm1', '1728.bp1', '2592.ex1', '2592.fc1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [24198, 36, 16080, 10368], 'label': '31104.fx.864.gr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fx1', 'old_label': '864.gr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gr1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246891
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '6.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.c1'], 'contains': ['12.m1', '12.p1', '12.u1', '18.y1', '18.ba1', '18.bd1', '96.x1'], 'core': '36.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [10405, 18144, 16080, 10368, 15552, 12138, 24268, 18576, 16056, 22752], 'label': '31104.fx.6.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1', 'old_label': '6.k1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.k1', 'subgroup_fusion': None, 'weyl_group': '1728.46101'}
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id: 186246892
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '48.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.t1', '16.b1', '24.c1'], 'contains': ['96.l1', '144.bs1', '144.bt1', '144.bu1', '144.bz1', '144.ce1', '144.cg1', '192.p1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [10405, 18648, 16080, 22752, 15552, 10368, 12460], 'label': '31104.fx.48.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1', 'old_label': '48.n1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.n1', 'subgroup_fusion': None, 'weyl_group': '144.189'}
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id: 186246893
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.gs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ec1', '288.cw1', '288.dc1', '432.bd1'], 'contains': ['1728.t1', '1728.cf1', '1728.dc1', '2592.ey1', '2592.fd1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [1, 36, 12940, 10368], 'label': '31104.fx.864.gs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.bd1', 'old_label': '864.gs1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gs1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246894
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.gt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ed1', '216.ju1', '288.cw1', '288.dd1', '432.oj1'], 'contains': ['1728.u1', '1728.cg1', '1728.dd1', '2592.ez1', '2592.fd1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [20737, 36, 16080, 22752], 'label': '31104.fx.864.gt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.oj1', 'old_label': '864.gt1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gt1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246895
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.gu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ee1', '216.jv1', '288.cw1', '288.dd1', '288.de1', '432.ok1'], 'contains': ['1728.v1', '1728.ch1', '1728.de1', '2592.ez1', '2592.fd1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [1, 36, 16080, 10368], 'label': '31104.fx.864.gu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.ok1', 'old_label': '864.gu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gu1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246896
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.gv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.eh1', '288.cx1', '288.dc1', '432.be1'], 'contains': ['1728.w1', '1728.cl1', '1728.dh1', '2592.ey1', '2592.fe1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [20737, 36, 10924, 2016], 'label': '31104.fx.864.gv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.be1', 'old_label': '864.gv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gv1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246897
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.gw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.ei1', '288.cx1', '288.dc1', '288.df1', '432.bf1'], 'contains': ['1728.x1', '1728.cm1', '1728.di1', '2592.ey1', '2592.fe1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [20737, 36, 556, 12384], 'label': '31104.fx.864.gw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.bf1', 'old_label': '864.gw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gw1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246898
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.gx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ej1', '216.ek1', '216.jw1', '288.cx1', '288.dd1'], 'contains': ['1728.y1', '1728.cn1', '1728.dj1', '2592.ez1', '2592.fe1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 1728, 'diagramx': None, 'generators': [20737, 36, 16080, 12384], 'label': '31104.fx.864.gx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '864.gx1', 'old_label': '864.gx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gx1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246899
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.gy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.co1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.cy1', '288.dg1', '432.hx1', '432.ol1'], 'contains': ['1728.z1', '1728.bc1', '1728.ca1', '2592.fa1', '2592.fb1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [26047, 36, 12096, 10368], 'label': '31104.fx.864.gy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.di1', 'old_label': '864.gy1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gy1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
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id: 186246900
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.gz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cn1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.da1', '288.dg1', '432.hy1', '432.hz1', '432.ol1'], 'contains': ['1728.z1', '1728.bf1', '1728.bo1', '2592.fb1', '2592.fc1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [6, 36, 12096, 10368], 'label': '31104.fx.864.gz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.gj1', 'old_label': '864.gz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gz1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246901
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.ha1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.kz1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.cz1', '288.db1', '288.dg1', '432.ia1', '432.om1'], 'contains': ['1728.ba1', '1728.bj1', '1728.bu1', '2592.fa1', '2592.fc1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [24198, 36, 22752, 10368], 'label': '31104.fx.864.ha1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.dj1', 'old_label': '864.ha1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ha1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246902
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.hb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.dc1', '288.dd1', '288.dh1', '432.bj1', '432.ib1', '432.om1'], 'contains': ['1728.ba1', '1728.cd1', '1728.dg1', '2592.fd1', '2592.fe1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1, 36, 22752, 10368], 'label': '31104.fx.864.hb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.d1', 'old_label': '864.hb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.hb1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246903
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '48.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.u1', '16.b1'], 'contains': ['96.m1', '144.bu1', '144.bv1', '144.bw1', '144.bx1', '144.ca1', '192.q1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [10405, 18648, 22752, 10368, 15552, 12460, 9168], 'label': '31104.fx.48.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.o1', 'old_label': '48.o1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.o1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
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id: 186246904
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.hc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.de1', '288.dh1', '432.bk1', '432.ic1', '432.ol1'], 'contains': ['1728.z1', '1728.ce1', '1728.da1', '2592.fd1', '2592.ff1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1, 36, 1728, 10368], 'label': '31104.fx.864.hc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '864.hc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.hc1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246905
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.hd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.df1', '288.dh1', '432.bl1', '432.bm1', '432.id1'], 'contains': ['1728.bb1', '1728.ck1', '1728.db1', '2592.fe1', '2592.ff1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [20737, 36, 1728, 12384], 'label': '31104.fx.864.hd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.q1', 'old_label': '864.hd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.hd1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246906
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.he1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cy1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.di1', '288.dk1', '432.il1', '432.ol1', '432.on1'], 'contains': ['1728.bc1', '1728.bo1', '1728.ce1', '2592.fg1', '2592.fh1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [26485, 12138, 22752, 12096], 'label': '31104.fx.864.he1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.hw1', 'old_label': '864.he1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.he1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186246907
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.hf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.kr1', '288.di1', '288.dj1', '288.dl1', '432.ok1'], 'contains': ['1728.bd1', '1728.bp1', '1728.ch1', '2592.fg1', '2592.fi1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [26485, 30714, 22752, 28012], 'label': '31104.fx.864.hf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.ok1', 'old_label': '864.hf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.hf1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186246908
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.hg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ks1', '288.di1', '288.dm1'], 'contains': ['1728.be1', '1728.bt1', '1728.cj1', '2592.fg1', '2592.fj1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 1728, 'diagramx': None, 'generators': [13861, 6, 10368, 19536], 'label': '31104.fx.864.hg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '864.hg1', 'old_label': '864.hg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.hg1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186246909
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.hh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.co1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.dn1', '432.hx1', '432.in1', '432.on1'], 'contains': ['1728.bc1', '1728.ca1', '1728.cx2', '2592.fk1', '2592.fl1', '2592.fl2'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [26047, 18612, 12096, 10368], 'label': '31104.fx.864.hh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.gi1', 'old_label': '864.hh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.hh1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246910
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.hi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.z1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ku1', '288.dj1', '288.dp1', '432.oj1'], 'contains': ['1728.bg1', '1728.bn1', '1728.cg1', '2592.fg1', '2592.fn1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [7477, 18582, 10368, 5260], 'label': '31104.fx.864.hi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.oj1', 'old_label': '864.hi1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.hi1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186246911
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.hj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.dg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.dk1', '288.dl1', '288.dm1', '288.dp1', '432.iu1', '432.om1', '432.oo1'], 'contains': ['1728.bj1', '1728.bu1', '1728.cd1', '2592.fg1', '2592.fp1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [7477, 6, 10368, 22752], 'label': '31104.fx.864.hj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.hy1', 'old_label': '864.hj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.hj1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186246912
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.hk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.q1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.bl1', '288.dj1', '288.dr1', '432.oi1'], 'contains': ['1728.bk1', '1728.bv1', '1728.cq1', '2592.fi1', '2592.fn1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [12133, 6, 8212, 5712], 'label': '31104.fx.864.hk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fx1', 'old_label': '864.hk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.hk1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246913
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.hl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cn1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.dn1', '432.hy1', '432.iw1', '432.on1'], 'contains': ['1728.bf1', '1728.bo1', '1728.cx2', '2592.fl1', '2592.fo1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [6, 18612, 12096, 10368], 'label': '31104.fx.864.hl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.gj1', 'old_label': '864.hl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.hl1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246914
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '48.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1', '24.h1', '24.j1'], 'contains': ['96.h1', '144.ch1', '144.ci1', '144.ci2', '144.cj1', '192.r1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [16020, 2016, 12096, 10924, 10368, 72, 18144], 'label': '31104.fx.48.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.p1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.p1', 'subgroup_fusion': None, 'weyl_group': '1296.2940'}
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id: 186246915
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.hl2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.dn1', '432.hz1', '432.iv1', '432.iw1'], 'contains': ['1728.bf1', '1728.bo1', '1728.cx1', '2592.fl2', '2592.fo1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [6, 16092, 12096, 10368], 'label': '31104.fx.864.hl2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.kc1', 'old_label': '864.hl2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.hl2', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246916
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.hm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cr1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.dn1', '432.ia1', '432.ix1', '432.oo1'], 'contains': ['1728.bj1', '1728.bu1', '1728.cy1', '2592.fk1', '2592.fo1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [24198, 16092, 22752, 10368], 'label': '31104.fx.864.hm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.gk1', 'old_label': '864.hm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.hm1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246917
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.hn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.db1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.dk1', '288.dq1', '432.iz1', '432.ol1', '432.on1'], 'contains': ['1728.bf1', '1728.ca1', '1728.ce1', '2592.fh1', '2592.fp1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [26485, 12138, 12096, 10368], 'label': '31104.fx.864.hn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.di1', 'old_label': '864.hn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.hn1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246918
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.ho1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.bc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.lh1', '288.dl1', '288.dr1', '432.oj1'], 'contains': ['1728.bh1', '1728.cb1', '1728.cg1', '2592.fi1', '2592.fp1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [26485, 30714, 28012, 10368], 'label': '31104.fx.864.ho1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fz1', 'old_label': '864.ho1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ho1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246919
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.hp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.li1', '288.dm1', '288.ds1'], 'contains': ['1728.bi1', '1728.cc1', '1728.cj2', '2592.fj1', '2592.fp1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 576, 'diagramx': None, 'generators': [13861, 6, 19536, 22752], 'label': '31104.fx.864.hp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.dm1', 'old_label': '864.hp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.hp1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246920
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.hq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cz1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.do1', '288.dt1', '432.jp1', '432.ol1', '432.on1'], 'contains': ['1728.bc1', '1728.bf1', '1728.da1', '2592.fm1', '2592.fq1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [5713, 12138, 12096, 10368], 'label': '31104.fx.864.hq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.hw1', 'old_label': '864.hq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.hq1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186246921
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.hr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ln1', '288.du1', '288.dv1', '432.oj1'], 'contains': ['1728.bg1', '1728.bh1', '1728.dd1', '2592.fq1', '2592.fr1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [1, 12138, 5712, 22752], 'label': '31104.fx.864.hr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.oj1', 'old_label': '864.hr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.hr1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246922
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.hs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.di1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.do1', '288.dv1', '432.jr1', '432.om1', '432.oo1'], 'contains': ['1728.bj1', '1728.dg1', '2592.fq1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [5713, 12138, 22752, 10368], 'label': '31104.fx.864.hs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.di1', 'old_label': '864.hs1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.hs1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246925
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '48.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.v1', '16.c1', '24.d1'], 'contains': ['96.d1', '96.f1', '96.g1', '144.cm1', '144.cn1', '144.cp1', '144.ct1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [1, 10368, 10924, 3096, 12384, 12096, 15552], 'label': '31104.fx.48.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.d1', 'old_label': '48.q1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.q1', 'subgroup_fusion': None, 'weyl_group': '648.610'}
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id: 186246926
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.hv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.lm1', '288.dp1', '288.dq1', '288.dr1', '288.ds1', '432.ok1'], 'contains': ['1728.bm1', '1728.bq1', '1728.ch1', '2592.fn1', '2592.fp1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [7477, 18582, 5260, 22752], 'label': '31104.fx.864.hv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fz1', 'old_label': '864.hv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.hv1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246927
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.hw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.lp1', '288.dt1', '288.du1', '288.dv1', '432.ok1'], 'contains': ['1728.bd1', '1728.bm1', '1728.de1', '2592.fq1', '2592.fr1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [1, 12138, 5712, 10368], 'label': '31104.fx.864.hw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fy1', 'old_label': '864.hw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.hw1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
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id: 186246928
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.hx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.lz1', '288.dx1', '288.dy1', '288.dz1', '432.ok1'], 'contains': ['1728.bp1', '1728.bq1', '1728.de1', '2592.fs1', '2592.ft1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [1, 6, 5712, 10368], 'label': '31104.fx.864.hx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.ok1', 'old_label': '864.hx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.hx1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246929
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.hy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ma1', '288.dw1', '288.dy1', '288.ea1'], 'contains': ['1728.br1', '1728.bs1', '1728.df1', '2592.fs1', '2592.fu1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 1728, 'diagramx': None, 'generators': [1, 22758, 28464, 10368], 'label': '31104.fx.864.hy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '864.hy1', 'old_label': '864.hy1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.hy1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246930
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.hz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.dy1', '288.eb1', '432.kh1', '432.om1', '432.oo1'], 'contains': ['1728.bu1', '1728.dg1', '2592.fs1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [5713, 6, 22752, 10368], 'label': '31104.fx.864.hz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.hy1', 'old_label': '864.hz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.hz1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246931
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.ia1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.bz1', '288.dx1', '432.oi1'], 'contains': ['1728.bv1', '1728.dn1', '2592.ft1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [1, 6, 8212, 5712], 'label': '31104.fx.864.ia1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.oi1', 'old_label': '864.ia1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ia1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246932
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.ib1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.ca1', '288.dw1'], 'contains': ['1728.bw1', '1728.do1', '2592.fu1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [1, 22758, 18580, 28464], 'label': '31104.fx.864.ib1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '864.ib1', 'old_label': '864.ib1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ib1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246933
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.ic1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.cb1', '288.dw1', '288.dx1'], 'contains': ['1728.bx1', '1728.by1', '1728.dp1', '2592.ft1', '2592.fu1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 1728, 'diagramx': None, 'generators': [1, 22758, 8212, 28464], 'label': '31104.fx.864.ic1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '864.ic1', 'old_label': '864.ic1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ic1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246934
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.id1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.cc1', '288.dw1'], 'contains': ['1728.bz1', '1728.dr2', '2592.fu1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [1, 14406, 18580, 19248], 'label': '31104.fx.864.id1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '864.id1', 'old_label': '864.id1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.id1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246935
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.ie1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.mc1', '288.dw1', '288.dx1', '288.dy1', '432.oj1'], 'contains': ['1728.bn1', '1728.cb1', '1728.dd1', '2592.fs1', '2592.ft1', '2592.fu1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [1, 6, 5712, 22752], 'label': '31104.fx.864.ie1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.oj1', 'old_label': '864.ie1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ie1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246936
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '48.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1', '24.e1', '24.g1', '24.k1'], 'contains': ['96.h1', '144.cm1', '144.co1', '144.cq1', '144.cu1', '192.s1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [1, 72, 12384, 12096, 18144, 10924, 10368], 'label': '31104.fx.48.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1', 'old_label': '48.r1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.r1', 'subgroup_fusion': None, 'weyl_group': '1296.2940'}
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id: 186246937
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.if1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.dz1', '288.ea1', '288.eb1', '432.kp1', '432.ol1', '432.on1'], 'contains': ['1728.bo1', '1728.ca1', '1728.da1', '2592.fs1', '2592.fv1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [5713, 6, 12096, 10368], 'label': '31104.fx.864.if1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.hw1', 'old_label': '864.if1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.if1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246938
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.ig1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.ec1', '288.ed1', '432.bj1', '432.br1', '432.kr1'], 'contains': ['1728.cd1', '1728.cv1', '1728.dg1', '2592.fw1', '2592.fx1', '2592.fx2'], 'core': '3456.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1, 18180, 22752, 10368], 'label': '31104.fx.864.ig1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.o1', 'old_label': '864.ig1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ig1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 186246939
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.ih1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.ee1', '432.br1', '432.ib1', '432.oo1'], 'contains': ['1728.cd1', '1728.cy1', '1728.dg1', '2592.fy1', '2592.fz1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1, 2628, 22752, 10368], 'label': '31104.fx.864.ih1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.d1', 'old_label': '864.ih1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ih1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246940
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.ii1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.eq1', '288.ec1', '432.bd1'], 'contains': ['1728.cf1', '1728.cr1', '1728.dc1', '2592.fw1', '2592.ga1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [1, 15588, 12940, 10368], 'label': '31104.fx.864.ii1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.bd1', 'old_label': '864.ii1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ii1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246941
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.ij1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.er1', '288.ec1', '432.be1'], 'contains': ['1728.cl1', '1728.cs1', '1728.dh1', '2592.fx1', '2592.ga1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [20737, 15588, 10924, 2016], 'label': '31104.fx.864.ij1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.be1', 'old_label': '864.ij1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ij1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246942
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.ik1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.es1', '288.ec1', '288.ef1', '432.bf1'], 'contains': ['1728.cm1', '1728.ct1', '1728.di1', '2592.fx2', '2592.ga1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [20737, 15588, 556, 12384], 'label': '31104.fx.864.ik1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.bf1', 'old_label': '864.ik1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ik1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246943
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.il1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.ed1', '432.bk1', '432.bx1', '432.ku1'], 'contains': ['1728.ce1', '1728.cu1', '1728.da1', '2592.fw1', '2592.gb1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [20737, 18180, 1728, 22752], 'label': '31104.fx.864.il1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.p1', 'old_label': '864.il1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.il1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246944
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.im1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.ed1', '288.ef1', '432.bl1', '432.bz1', '432.kv1'], 'contains': ['1728.ck1', '1728.cw1', '1728.db1', '2592.fx2', '2592.gb1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [20737, 15588, 1728, 12384], 'label': '31104.fx.864.im1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.q1', 'old_label': '864.im1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.im1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246945
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.im2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.ed1', '432.bm1', '432.by1', '432.kv1'], 'contains': ['1728.ck1', '1728.cw3', '1728.db1', '2592.fx1', '2592.gb1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [20737, 18180, 1728, 12384], 'label': '31104.fx.864.im2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.q1', 'old_label': '864.im2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.im2', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246946
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.in1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.ee1', '432.bx1', '432.ic1', '432.on1'], 'contains': ['1728.ce1', '1728.cx2', '1728.da1', '2592.fy1', '2592.gc1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1, 2628, 1728, 10368], 'label': '31104.fx.864.in1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '864.in1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.in1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246947
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '48.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.w1', '16.c1', '24.f1'], 'contains': ['96.i1', '144.ck1', '144.cl1', '144.cm1', '144.cv1', '192.t1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [1, 18648, 22752, 12096, 15552, 76, 10368], 'label': '31104.fx.48.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '48.s1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.s1', 'subgroup_fusion': None, 'weyl_group': '1296.2940'}
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id: 186246948
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '864.io1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.ee1', '432.by1', '432.bz1', '432.id1'], 'contains': ['1728.ck1', '1728.cz1', '1728.db1', '2592.fz1', '2592.gc1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [20737, 2628, 1728, 12384], 'label': '31104.fx.864.io1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.q1', 'old_label': '864.io1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.io1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246949
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '972.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.a1', '324.c1', '486.b1'], 'contains': ['1944.d1', '1944.e1', '1944.h1', '1944.k1', '1944.m1', '1944.bn1', '1944.bp1', '1944.br1', '1944.bt1', '1944.cb1', '1944.cf1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [5713, 24198, 36, 18648], 'label': '31104.fx.972.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '972.a1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186246950
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '972.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.b1', '324.d1', '486.b1'], 'contains': ['1944.d1', '1944.f1', '1944.j1', '1944.l1', '1944.n1', '1944.bo1', '1944.bq1', '1944.bs1', '1944.bu1', '1944.cc1', '1944.cg1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [8305, 24198, 36, 18648], 'label': '31104.fx.972.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '972.b1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186246951
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '972.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.e1', '324.g1', '486.b1'], 'contains': ['1944.h1', '1944.i1', '1944.l1', '1944.n1', '1944.p1', '1944.bv1', '1944.bx1', '1944.bz1', '1944.cd1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [8305, 24198, 2628, 18648], 'label': '31104.fx.972.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '972.c1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.c1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
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id: 186246952
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '972.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.f1', '324.h1', '486.b1'], 'contains': ['1944.i1', '1944.j1', '1944.k1', '1944.m1', '1944.t1', '1944.bw1', '1944.by1', '1944.ca1', '1944.ce1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [5713, 24198, 2628, 18648], 'label': '31104.fx.972.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '972.d1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.d1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
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id: 186246953
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '972.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cm1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.i1', '324.j1', '324.k1', '324.l1', '486.a1', '486.b1', '486.g1'], 'contains': ['1944.d1', '1944.i1', '1944.v1', '1944.w1', '1944.x1', '1944.ch1', '1944.ci1', '1944.ck1', '1944.cl1', '1944.cq1', '1944.cu1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [19135, 36, 16056, 2592], 'label': '31104.fx.972.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '972.e1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.e1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
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id: 186246954
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '972.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.m1', '324.n1', '324.o1', '486.b1', '486.c1', '486.h1'], 'contains': ['1944.e1', '1944.f1', '1944.p1', '1944.t1', '1944.v1', '1944.y1', '1944.ba1', '1944.cj1', '1944.cw1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [20737, 36, 18576, 18144], 'label': '31104.fx.972.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '972.f1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.f1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 186246955
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '972.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cm1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.p1', '324.q1', '324.t1', '324.u1', '486.a1', '486.c1', '486.g1'], 'contains': ['1944.v1', '1944.bb1', '1944.bd1', '1944.ck1', '1944.cx1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [3583, 36, 16056], 'label': '31104.fx.972.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '972.g1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.g1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
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id: 186246956
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '972.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.r1', '324.s1', '324.v1', '486.a1', '486.h1'], 'contains': ['1944.g1', '1944.u1', '1944.v1', '1944.bc1', '1944.be1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [5689, 36, 18576], 'label': '31104.fx.972.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '972.h1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.h1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
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id: 186246957
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '972.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ct1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.w1', '324.x1', '324.bg1', '486.b1', '486.d1', '486.i1'], 'contains': ['1944.h1', '1944.j1', '1944.w1', '1944.x1', '1944.y1', '1944.cm1', '1944.cn1', '1944.cp1', '1944.cs1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [26485, 12138, 16056, 2592], 'label': '31104.fx.972.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '972.i1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.i1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
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id: 186246958
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '48.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1', '16.c1', '24.c1'], 'contains': ['96.l1', '144.cr1', '144.cs1', '144.ct1', '144.cu1', '144.cv1', '144.cw1', '144.cx1', '144.cy1', '144.cz1', '192.u1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [1, 18648, 10368, 76, 15552, 5712, 22752], 'label': '31104.fx.48.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1', 'old_label': '48.t1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.t1', 'subgroup_fusion': None, 'weyl_group': None}
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id: 186246959
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '972.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cm1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.y1', '324.z1', '324.ba1', '324.bh1', '486.d1', '486.e1', '486.g1'], 'contains': ['1944.w1', '1944.z1', '1944.bd1', '1944.cq1', '1944.cx1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [8646, 15588, 18144], 'label': '31104.fx.972.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '972.j1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.j1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
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id: 186246960
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '972.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ct1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.bb1', '324.bd1', '324.bi1', '486.a1', '486.e1', '486.i1'], 'contains': ['1944.w1', '1944.bc1', '1944.bd1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [10933, 12138], 'label': '31104.fx.972.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '972.k1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.k1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
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id: 186246961
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '972.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cv1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.bc1', '324.be1', '324.bj1', '486.a1', '486.d1', '486.j1'], 'contains': ['1944.w1', '1944.bb1', '1944.be1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [21265, 27690], 'label': '31104.fx.972.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '972.l1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.l1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
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id: 186246962
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '972.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cv1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.bf1', '324.bk1', '486.b1', '486.e1', '486.j1'], 'contains': ['1944.k1', '1944.l1', '1944.w1', '1944.ba1', '1944.co1', '1944.cr1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [5713, 12138, 16056, 2592], 'label': '31104.fx.972.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '972.m1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.m1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
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id: 186246963
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '972.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cm1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.bl1', '324.bo1', '324.bp1', '324.bq1', '486.d1', '486.f1', '486.g1'], 'contains': ['1944.x1', '1944.z1', '1944.bb1', '1944.cu1', '1944.cx1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [19135, 15588, 16056], 'label': '31104.fx.972.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '972.n1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.n1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
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id: 186246964
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '972.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ct1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.bm1', '324.br1', '324.bt1', '486.a1', '486.f1', '486.i1'], 'contains': ['1944.x1', '1944.bb1', '1944.bc1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [23029, 6], 'label': '31104.fx.972.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '972.o1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.o1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
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id: 186246965
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '972.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.bn1', '324.bs1', '324.bu1', '486.a1', '486.d1', '486.k1'], 'contains': ['1944.x1', '1944.bd1', '1944.be1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [21265, 6], 'label': '31104.fx.972.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '972.p1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.p1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
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id: 186246966
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '972.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.bv1', '324.bw1', '486.b1', '486.f1', '486.k1'], 'contains': ['1944.m1', '1944.n1', '1944.x1', '1944.ba1', '1944.ct1', '1944.cv1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [5713, 6, 16056, 2592], 'label': '31104.fx.972.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '972.q1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.q1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
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id: 186247420
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.er1', '576.y1', '576.bg1', '864.ic1'], 'contains': ['3456.t1', '5184.ba1', '5184.bf1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 576, 'diagramx': None, 'generators': [26047, 8304, 3100], 'label': '31104.fx.1728.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.dw1', 'old_label': '1728.bx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.bx1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186246967
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '972.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.bx1', '324.by1', '324.cb1', '486.d1', '486.h1'], 'contains': ['1944.o1', '1944.r1', '1944.y1', '1944.z1', '1944.be1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [5689, 16092, 18576], 'label': '31104.fx.972.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '972.r1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.r1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
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id: 186246968
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '972.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ct1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.bz1', '324.ca1', '324.cc1', '486.c1', '486.d1', '486.i1'], 'contains': ['1944.y1', '1944.bb1', '1944.bd1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [26485, 27690], 'label': '31104.fx.972.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '972.s1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.s1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
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id: 186246969
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '48.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.df1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1', '24.i1', '24.j1', '24.k1', '24.l1', '24.m1', '24.n1'], 'contains': ['96.h1', '144.da1', '144.db1', '144.dc1', '144.dd1', '144.de1', '144.df1', '144.dg1', '192.a1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [3024, 18216, 12384, 10924, 18144, 12096, 10368], 'label': '31104.fx.48.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.u1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.u1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186246970
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '972.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.cd1', '324.ce1', '324.cf1', '486.e1', '486.f1', '486.h1'], 'contains': ['1944.q1', '1944.s1', '1944.z1', '1944.ba1', '1944.bc1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [20737, 16092, 18576], 'label': '31104.fx.972.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '972.t1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.t1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
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id: 186246971
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '972.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cv1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.cg1', '324.ci1', '486.c1', '486.f1', '486.j1'], 'contains': ['1944.ba1', '1944.bb1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [5713, 27690], 'label': '31104.fx.972.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '972.u1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.u1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
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id: 186246972
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '972.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.ch1', '324.cj1', '486.c1', '486.e1', '486.k1'], 'contains': ['1944.ba1', '1944.bd1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [5713, 15558], 'label': '31104.fx.972.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '972.v1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.v1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
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id: 186246973
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '972.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.ck1', '324.cm1', '324.cn1', '324.co1', '324.cp1', '486.h1'], 'contains': ['1944.b1', '1944.c1', '1944.e1', '1944.g1', '1944.o1', '1944.q1', '1944.bf1', '1944.bg1', '1944.bh1', '1944.bi1', '1944.bk1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [20737, 36, 16056, 2592], 'label': '31104.fx.972.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.h1', 'old_label': '972.w1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.w1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 186246974
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '972.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.cl1', '324.cq1', '324.cr1', '324.cs1', '324.ct1', '486.h1'], 'contains': ['1944.f1', '1944.g1', '1944.r1', '1944.s1', '1944.bh1', '1944.bl1', '1944.bm1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [21169, 36, 16056], 'label': '31104.fx.972.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.h1', 'old_label': '972.x1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.x1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186246975
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '972.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.cu1', '324.cv1', '324.cw1', '324.cx1', '324.cy1', '486.h1'], 'contains': ['1944.o1', '1944.p1', '1944.s1', '1944.u1', '1944.bi1', '1944.bj1', '1944.bm1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [21169, 468, 16056], 'label': '31104.fx.972.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.h1', 'old_label': '972.y1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.y1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186246976
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '972.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.cz1', '324.da1', '324.db1', '324.dc1', '324.dd1', '486.h1'], 'contains': ['1944.q1', '1944.r1', '1944.t1', '1944.u1', '1944.bj1', '1944.bk1', '1944.bl1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [20737, 468, 16056], 'label': '31104.fx.972.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.h1', 'old_label': '972.z1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.z1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186246977
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '972.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.de1', '324.df1', '324.dg1', '324.dh1', '324.di1', '486.g1', '486.h1'], 'contains': ['1944.a1', '1944.v1', '1944.z1', '1944.bh1', '1944.bj1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [36, 16056, 18576, 15552, 18144], 'label': '31104.fx.972.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '972.ba1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.ba1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246978
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '972.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.lz1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.dj1', '324.dk1', '324.dl1', '324.dm1', '324.dn1', '324.do1', '486.g1', '486.i1', '486.j1'], 'contains': ['1944.a1', '1944.w1', '1944.bb1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [17371, 16056, 15552], 'label': '31104.fx.972.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '972.bb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bb1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186246979
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '972.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.jw1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.dp1', '324.dq1', '324.dr1', '324.ds1', '324.dt1', '324.du1', '324.dv1', '324.dw1', '486.g1', '486.i1', '486.k1'], 'contains': ['1944.a1', '1944.x1', '1944.bd1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [6, 18144, 15552], 'label': '31104.fx.972.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '972.bc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bc1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186246980
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '48.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.a1', '24.q1', '24.r1', '24.s1'], 'contains': ['96.n1', '144.ep1', '144.eq1', '144.er1', '144.es1', '192.d1'], 'core': '576.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [36, 22752, 12096, 20760, 10368, 15624, 432], 'label': '31104.fx.48.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.x1', 'old_label': '48.v1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.v1', 'subgroup_fusion': None, 'weyl_group': '2592.jb'}
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id: 186246981
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '972.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.cx1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.dx1', '324.dy1', '324.dz1', '324.ea1', '324.eb1', '324.ec1', '324.ed1', '486.h1', '486.i1'], 'contains': ['1944.a1', '1944.y1', '1944.bc1', '1944.bi1', '1944.bl1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [10405, 16056, 18576], 'label': '31104.fx.972.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '972.bd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bd1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
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id: 186246982
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '972.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.cp1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.ee1', '324.ef1', '324.eg1', '324.eh1', '324.ei1', '324.ej1', '324.ek1', '486.h1', '486.j1', '486.k1'], 'contains': ['1944.a1', '1944.ba1', '1944.be1', '1944.bk1', '1944.bm1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1, 16056, 18576], 'label': '31104.fx.972.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '972.be1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.be1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
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id: 186246983
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '972.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.em1', '324.en1', '324.eo1', '486.b1'], 'contains': ['1944.bn1', '1944.bo1', '1944.br1', '1944.bs1', '1944.bx1', '1944.by1', '1944.cd1', '1944.ce1', '1944.ch1', '1944.cj1', '1944.ck1', '1944.cn1', '1944.co1', '1944.cs1', '1944.ct1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [5713, 21606, 36, 16056], 'label': '31104.fx.972.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '972.bf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bf1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186246984
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '972.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.be1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.el1', '324.ep1', '324.eq1', '324.er1', '486.b1'], 'contains': ['1944.bn1', '1944.bo1', '1944.bp1', '1944.bq1', '1944.bv1', '1944.bw1', '1944.bz1', '1944.ca1', '1944.ch1', '1944.ci1', '1944.cj1', '1944.cm1', '1944.cp1', '1944.cr1', '1944.cv1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [5713, 24198, 36, 2592], 'label': '31104.fx.972.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '972.bg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bg1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186246985
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '972.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.es1', '324.et1', '324.ev1', '486.b1'], 'contains': ['1944.bt1', '1944.bu1', '1944.bv1', '1944.bw1', '1944.cd1', '1944.ce1', '1944.cf1', '1944.cg1', '1944.cl1', '1944.cm1', '1944.co1', '1944.cs1', '1944.cu1', '1944.cv1', '1944.cw1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [5713, 24198, 2628, 16056], 'label': '31104.fx.972.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '972.bh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bh1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
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id: 186247421
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.es1', '576.z1', '576.bf1', '864.ic1'], 'contains': ['3456.t1', '5184.bb1', '5184.be1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 576, 'diagramx': None, 'generators': [26047, 31056, 23836], 'label': '31104.fx.1728.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.dx1', 'old_label': '1728.by1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.by1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186246986
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '972.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.eu1', '324.ew1', '324.ex1', '486.b1'], 'contains': ['1944.bt1', '1944.bu1', '1944.bx1', '1944.by1', '1944.bz1', '1944.ca1', '1944.cb1', '1944.cc1', '1944.cl1', '1944.cn1', '1944.cp1', '1944.cq1', '1944.cr1', '1944.ct1', '1944.cw1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [5713, 24270, 108, 2592], 'label': '31104.fx.972.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '972.bi1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bi1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
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id: 186246987
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1152.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': ['27.a1'], 'conjugacy_class_count': 1, 'contained_in': ['384.a1', '384.b1', '576.a1', '576.b1', '576.i1', '576.r1', '576.bj1', '576.bm1', '576.bz1', '576.ca1', '576.cd1'], 'contains': ['3456.a1', '3456.b1', '3456.i1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [12096, 22752, 10368], 'label': '31104.fx.1152.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1152.a1', 'normal_contained_in': ['72.a1', '576.a1'], 'normal_contains': ['3456.a1'], 'normalizer': '1.a1', 'old_label': '1152.a1', 'projective_image': '31104.fx', 'quotient_action_image': '72.46', 'quotient_action_kernel': '16.14', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '1152.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186246988
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1152.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.bj1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.bc1', '288.cn1', '288.co1', '384.b1', '576.l1', '576.p1', '576.u1', '576.bb1', '576.bc1', '576.br1', '576.cb1'], 'contains': ['3456.b1', '3456.e1', '3456.h1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [5712, 12096], 'label': '31104.fx.1152.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bd1', 'old_label': '1152.b1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246989
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1152.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.bd1', '288.cp1', '288.cq1', '384.b1', '576.bd1', '576.be1', '576.cc1'], 'contains': ['3456.b1', '3456.f1', '3456.h1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [28464, 12096], 'label': '31104.fx.1152.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.bb1', 'old_label': '1152.c1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.c1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246990
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1152.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.be1', '384.d1', '576.y1', '576.bf1', '576.cg1'], 'contains': ['3456.c1', '3456.d1', '3456.f1', '3456.p1', '3456.q1', '3456.s1', '3456.t1', '3456.v1', '3456.v2'], 'core': '10368.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [18580, 28464, 10368], 'label': '31104.fx.1152.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.ba1', 'old_label': '1152.d1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186246991
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '48.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.l1', '24.q1', '24.t1', '24.v1'], 'contains': ['96.n1', '144.et1', '144.ev1', '144.ew1', '144.ex1', '192.e1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [17371, 2592, 15984, 5712, 22752, 12096, 10368], 'label': '31104.fx.48.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.x1', 'old_label': '48.w1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.w1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
-
id: 186246992
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1152.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.bf1', '384.d1', '576.j1', '576.q1', '576.v1', '576.z1', '576.bg1', '576.bs1', '576.ch1'], 'contains': ['3456.c1', '3456.d1', '3456.e1', '3456.p1', '3456.r1', '3456.t1', '3456.u1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [8212, 5712, 22752], 'label': '31104.fx.1152.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bc1', 'old_label': '1152.e1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.e1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186246993
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1152.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.bg1', '384.e1', '576.w1', '576.bh1', '576.bt1'], 'contains': ['3456.e1', '3456.g1', '3456.h2'], 'core': '10368.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [30964, 29904], 'label': '31104.fx.1152.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.x1', 'old_label': '1152.f1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.f1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246994
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1152.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.bh1', '384.e1', '576.bi1'], 'contains': ['3456.f1', '3456.g1', '3456.h2'], 'core': '10368.a1', 'coset_action_label': None, 'count': 384, 'diagramx': None, 'generators': [10228, 29904], 'label': '31104.fx.1152.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '192.k1', 'old_label': '1152.g1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.g1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
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id: 186246995
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1152.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.bk1', '384.a1', '384.c1', '384.d1', '576.c1', '576.m1', '576.bn1', '576.bx1', '576.ci1'], 'contains': ['3456.a1', '3456.c1', '3456.j1', '3456.k1', '3456.m1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [10924, 22752, 10368], 'label': '31104.fx.1152.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1', 'old_label': '1152.h1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.h1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186246996
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1152.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.bl1', '288.cs1', '384.b1', '384.d1', '384.e1', '576.n1', '576.s1', '576.x1', '576.ba1', '576.bk1', '576.bo1', '576.cj1'], 'contains': ['3456.a1', '3456.d1', '3456.e1', '3456.f1', '3456.l1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [5712, 22752, 10368], 'label': '31104.fx.1152.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.d1', 'old_label': '1152.i1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.i1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186246997
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1152.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.bn1', '384.a1', '384.c1', '384.e1', '576.d1', '576.bp1'], 'contains': ['3456.a1', '3456.g1', '3456.n1', '3456.n2'], 'core': '3456.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [11764, 22752, 10368], 'label': '31104.fx.1152.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1', 'old_label': '1152.j1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.j1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 186246998
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1152.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.bo1', '288.ct1', '384.b1', '384.c1', '384.e1', '576.t1', '576.bl1', '576.bq1'], 'contains': ['3456.a1', '3456.h1', '3456.h2', '3456.o1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [24268, 22752, 10368], 'label': '31104.fx.1152.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.d1', 'old_label': '1152.k1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.k1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186246999
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1152.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.df1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.bq1', '384.a1', '576.e1', '576.f1', '576.o1', '576.bu1', '576.by1', '576.by2', '576.ce1'], 'contains': ['3456.i1', '3456.k1', '3456.n2'], 'core': '31104.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [556, 12096], 'label': '31104.fx.1152.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.d1', 'old_label': '1152.l1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.l1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186247000
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1152.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.df1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.bs1', '384.a1', '576.g1', '576.h1', '576.cf1'], 'contains': ['3456.i1', '3456.m1', '3456.n2'], 'core': '31104.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [12096, 10924], 'label': '31104.fx.1152.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.q1', 'old_label': '1152.m1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.m1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
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id: 186247001
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1152.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.bt1', '288.bv1', '384.d1', '576.ck1'], 'contains': ['3456.j1', '3456.l1', '3456.m1', '3456.p1', '3456.q1', '3456.t1', '3456.u1', '3456.v1', '3456.v2'], 'core': '31104.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [18580, 5712, 12384], 'label': '31104.fx.1152.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '192.u1', 'old_label': '1152.n1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.n1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247002
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '6.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.d1', '3.b1'], 'contains': ['12.b1', '12.l1', '12.w1', '18.z1', '18.be1', '18.bg1', '24.v1'], 'core': '12.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1, 2592, 22752, 10368, 15552, 12138, 5712, 432, 16056, 12096], 'label': '31104.fx.6.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '6.l1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.l1', 'subgroup_fusion': None, 'weyl_group': '10368.je'}
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id: 186247003
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '48.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.b1', '24.r1', '24.u1', '24.v1'], 'contains': ['96.n1', '144.eu1', '144.ey1', '144.ez1', '144.fa1', '192.f1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [17371, 16056, 22752, 12096, 18576, 10368, 7780], 'label': '31104.fx.48.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.x1', 'old_label': '48.x1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.x1', 'subgroup_fusion': None, 'weyl_group': '864.4000'}
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id: 186247004
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1152.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.bu1', '288.bx1', '384.c1', '576.bv1'], 'contains': ['3456.k1', '3456.n1', '3456.o1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [8500, 29904], 'label': '31104.fx.1152.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '192.o1', 'old_label': '1152.o1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.o1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 186247005
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1152.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.bw1', '288.by1', '384.d1', '576.k1', '576.bw1', '576.cl1'], 'contains': ['3456.j1', '3456.k1', '3456.l1', '3456.p1', '3456.q1', '3456.r1', '3456.s1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [8212, 5712, 12384], 'label': '31104.fx.1152.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.p1', 'old_label': '1152.p1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.p1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247007
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.a1', '432.b1', '432.c1', '648.b1', '648.cn1', '648.em1'], 'contains': ['2592.a1', '2592.i1', '2592.be1', '2592.ct1', '2592.dj1', '3888.a1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [36, 16056, 15552, 22752], 'label': '31104.fx.1296.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.v1', 'old_label': '1296.a1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247008
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.c1', '432.d1', '432.e1', '648.c1', '648.co1', '648.eo1'], 'contains': ['2592.b1', '2592.j1', '2592.bf1', '2592.cu1', '2592.dk1', '3888.a1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [36, 16056, 15552, 12384], 'label': '31104.fx.1296.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.w1', 'old_label': '1296.b1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247009
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.c1', '432.f1', '432.g1', '648.d1', '648.co1', '648.en1'], 'contains': ['2592.c1', '2592.k1', '2592.bg1', '2592.cu1', '2592.dk2', '3888.a1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [36, 3024, 18216, 12384], 'label': '31104.fx.1296.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.w1', 'old_label': '1296.c1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.c1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247010
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.a1', '432.d1', '432.f1', '648.cq1', '648.ep1'], 'contains': ['2592.d1', '2592.m1', '2592.bi2', '2592.cv1', '2592.cx1', '2592.dl1', '2592.dn2', '3888.a1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [36, 18144, 18576, 12096], 'label': '31104.fx.1296.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.di1', 'old_label': '1296.d1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 186247011
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.a1', '432.e1', '432.g1', '648.cp1', '648.cr1', '648.eq1'], 'contains': ['2592.e1', '2592.l1', '2592.bh1', '2592.cw1', '2592.dm1', '3888.a1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [36, 16056, 2592, 12096], 'label': '31104.fx.1296.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.di1', 'old_label': '1296.e1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.e1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 186247012
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.b1', '432.e1', '432.f1', '648.e1', '648.cr1', '648.ep1'], 'contains': ['2592.f1', '2592.l1', '2592.bh2', '2592.cx1', '2592.dn3', '3888.a1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [36, 432, 72, 12096], 'label': '31104.fx.1296.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '1296.f1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.f1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 186247013
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.a1', '432.b1', '432.d1', '432.g1', '648.cq1', '648.cr1', '648.eq1'], 'contains': ['2592.g1', '2592.m1', '2592.bi1', '2592.cw1', '2592.cx1', '2592.dm2', '2592.dn1', '3888.a1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [36, 504, 2592, 12096], 'label': '31104.fx.1296.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.di1', 'old_label': '1296.g1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.g1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247014
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '48.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.n1', '24.q1', '24.u1', '24.w1'], 'contains': ['96.n1', '144.fb1', '144.fj1', '144.fk1', '144.fl1', '192.i1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [26047, 12096, 2592, 5712, 10368, 22752, 15984], 'label': '31104.fx.48.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.x1', 'old_label': '48.y1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.y1', 'subgroup_fusion': None, 'weyl_group': '864.4000'}
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id: 186247015
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.h1', '432.i1', '648.b1', '648.f1', '648.er1'], 'contains': ['2592.a1', '2592.n1', '2592.bp1', '3888.b1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [10405, 16056, 10368, 15552], 'label': '31104.fx.1296.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cr1', 'old_label': '1296.h1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.h1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247016
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.h1', '432.j1', '648.c1', '648.g1', '648.et1'], 'contains': ['2592.b1', '2592.o1', '2592.br1', '3888.b1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [10405, 16056, 12384, 15552], 'label': '31104.fx.1296.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cr1', 'old_label': '1296.i1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.i1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247017
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.h1', '432.k1', '648.d1', '648.h1', '648.es1'], 'contains': ['2592.c1', '2592.p1', '2592.bs1', '3888.b1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [10405, 2664, 12384, 18144], 'label': '31104.fx.1296.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cr1', 'old_label': '1296.j1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.j1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247018
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.i1', '432.j1', '432.k1', '648.e1', '648.i1', '648.eu1'], 'contains': ['2592.f1', '2592.q1', '2592.bv1', '3888.b1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [10405, 16056, 15552, 1728], 'label': '31104.fx.1296.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bc1', 'old_label': '1296.k1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.k1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247019
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.l1', '432.l2', '432.m1', '432.n1', '648.cn1', '648.dd1', '648.ey1'], 'contains': ['2592.a1', '2592.u1', '2592.be1', '2592.dj1', '2592.dt1', '2592.dt2', '3888.c1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [18612, 16056, 15552, 10368], 'label': '31104.fx.1296.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.dg1', 'old_label': '1296.l1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.l1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247020
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.n1', '432.o1', '432.p1', '648.co1', '648.de1', '648.fa1'], 'contains': ['2592.b1', '2592.v1', '2592.bf1', '2592.dk2', '2592.du1', '3888.c1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [3060, 16056, 15552, 12384], 'label': '31104.fx.1296.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.dh1', 'old_label': '1296.m1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.m1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247021
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.n1', '432.q1', '432.r1', '432.r2', '648.co1', '648.de1', '648.ez1'], 'contains': ['2592.c1', '2592.w1', '2592.bg1', '2592.dk1', '2592.du1', '3888.c1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [15588, 3024, 18216, 12384], 'label': '31104.fx.1296.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.dh1', 'old_label': '1296.n1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.n1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247022
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.l1', '432.l2', '432.o1', '432.q1', '648.cq1', '648.dg1', '648.fb1'], 'contains': ['2592.d1', '2592.y1', '2592.bi1', '2592.dl1', '2592.dn1', '2592.dv1', '2592.dx1', '3888.c1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [2628, 18144, 18576, 12096], 'label': '31104.fx.1296.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.di1', 'old_label': '1296.o1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.o1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247023
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.l1', '432.p1', '432.r2', '648.cr1', '648.df1', '648.fc1'], 'contains': ['2592.e1', '2592.x1', '2592.bh2', '2592.dm2', '2592.dw1', '3888.c1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [3060, 16056, 2592, 12096], 'label': '31104.fx.1296.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.di1', 'old_label': '1296.p1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.p1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247024
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.p2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.l2', '432.p1', '432.r1', '648.cp1', '648.dh1', '648.fc1'], 'contains': ['2592.e1', '2592.x2', '2592.bh1', '2592.dm1', '2592.dw2', '3888.c1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [18612, 16056, 2592, 12096], 'label': '31104.fx.1296.p2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.di1', 'old_label': '1296.p2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.p2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247025
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '48.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.d1', '24.r1', '24.t1', '24.w1'], 'contains': ['96.n1', '144.fc1', '144.fd1', '144.fe1', '144.ff1', '144.fg1', '144.fh1', '144.fi1', '192.l1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [26047, 16056, 22752, 18148, 18576, 12096, 10368], 'label': '31104.fx.48.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.x1', 'old_label': '48.z1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.z1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
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id: 186247026
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.m1', '432.p1', '432.q1', '648.cr1', '648.dh1', '648.fb1'], 'contains': ['2592.f1', '2592.x1', '2592.bh1', '2592.dn1', '2592.dx1', '3888.c1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [16020, 432, 72, 12096], 'label': '31104.fx.1296.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.di1', 'old_label': '1296.q1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.q1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247027
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.l1', '432.m1', '432.o1', '432.r1', '648.cr1', '648.dg1', '648.fc1'], 'contains': ['2592.g1', '2592.y2', '2592.bi1', '2592.dm1', '2592.dn3', '2592.dw1', '2592.dx1', '3888.c1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [16020, 15552, 16056, 12096], 'label': '31104.fx.1296.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.di1', 'old_label': '1296.r1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.r1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247028
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.r2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.l2', '432.m1', '432.o1', '432.r2', '648.cq1', '648.dh1', '648.fc1'], 'contains': ['2592.g1', '2592.y1', '2592.bi2', '2592.dm2', '2592.dn2', '2592.dw2', '2592.dx1', '3888.c1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [18612, 504, 2592, 12096], 'label': '31104.fx.1296.r2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.di1', 'old_label': '1296.r2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.r2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247029
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.s1', '432.t1', '432.u1', '648.f1', '648.dd1', '648.em1'], 'contains': ['2592.a1', '2592.u1', '2592.z1', '2592.dj1', '2592.do1', '3888.d1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [2628, 16056, 15552, 22752], 'label': '31104.fx.1296.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.v1', 'old_label': '1296.s1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.s1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247030
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.u1', '432.v1', '432.w1', '648.g1', '648.de1', '648.eo1'], 'contains': ['2592.b1', '2592.v1', '2592.ba1', '2592.dk1', '2592.dp1', '3888.d1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [18180, 16056, 15552, 12384], 'label': '31104.fx.1296.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.w1', 'old_label': '1296.t1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.t1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 186247031
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.u1', '432.x1', '432.y1', '648.h1', '648.de1', '648.en1'], 'contains': ['2592.c1', '2592.w1', '2592.bb1', '2592.dk2', '2592.dp1', '3888.d1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [16020, 3024, 18216, 12384], 'label': '31104.fx.1296.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.w1', 'old_label': '1296.u1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.u1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 186247032
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.s1', '432.v1', '432.x1', '648.dg1', '648.ep1'], 'contains': ['2592.d1', '2592.y2', '2592.bd1', '2592.dl1', '2592.dn3', '2592.dq1', '2592.ds1', '3888.d1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [108, 18144, 18576, 12096], 'label': '31104.fx.1296.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.di1', 'old_label': '1296.v1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.v1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 186247033
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.s1', '432.w1', '432.y1', '648.df1', '648.dh1', '648.eq1'], 'contains': ['2592.e1', '2592.x1', '2592.bc1', '2592.dm2', '2592.dr1', '3888.d1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [15588, 16056, 2592, 12096], 'label': '31104.fx.1296.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.di1', 'old_label': '1296.w1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.w1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247034
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.t1', '432.w1', '432.x1', '648.i1', '648.dh1', '648.ep1'], 'contains': ['2592.f1', '2592.x2', '2592.bc1', '2592.dn2', '2592.ds1', '3888.d1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [18612, 432, 72, 12096], 'label': '31104.fx.1296.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '1296.x1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.x1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247035
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.s1', '432.t1', '432.v1', '432.y1', '648.dg1', '648.dh1', '648.eq1'], 'contains': ['2592.g1', '2592.y1', '2592.bd1', '2592.dm1', '2592.dn1', '2592.dr1', '2592.ds1', '3888.d1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [18684, 504, 2592, 12096], 'label': '31104.fx.1296.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.di1', 'old_label': '1296.y1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.y1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247036
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '48.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.r1', '24.s1', '24.t1', '24.u1'], 'contains': ['96.n1', '144.fm1', '144.fn1', '144.fo1', '144.fp1', '192.n1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [10405, 18576, 10368, 22752, 2592, 16080, 1728], 'label': '31104.fx.48.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.x1', 'old_label': '48.ba1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ba1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
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id: 186247037
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.z1', '432.ba1', '432.bb1', '648.e1', '648.i1', '648.fd1'], 'contains': ['2592.f1', '2592.bj1', '2592.bw1', '3888.e1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1, 16056, 1728, 15552], 'label': '31104.fx.1296.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cp1', 'old_label': '1296.z1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.z1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247038
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.z1', '432.bc1', '648.b1', '648.f1', '648.fe1'], 'contains': ['2592.a1', '2592.bk1', '2592.bq1', '3888.e1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1, 16056, 15552, 10368], 'label': '31104.fx.1296.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cs1', 'old_label': '1296.ba1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ba1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247039
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ba1', '432.bc1', '648.c1', '648.g1', '648.fg1'], 'contains': ['2592.b1', '2592.bl1', '2592.bt1', '3888.e1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1, 16056, 15552, 12384], 'label': '31104.fx.1296.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cu1', 'old_label': '1296.bb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.bb1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247040
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.bb1', '432.bc1', '648.d1', '648.h1', '648.ff1'], 'contains': ['2592.c1', '2592.bm1', '2592.bu1', '3888.e1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1, 2664, 18144, 12384], 'label': '31104.fx.1296.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ct1', 'old_label': '1296.bc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.bc1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247041
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.ck1', '432.bd1', '432.be1', '432.bf1', '648.dz1'], 'contains': ['2592.h1', '2592.r1', '2592.bn1', '2592.ey1', '2592.ga1', '3888.f1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [20737, 36, 15552, 12940], 'label': '31104.fx.1296.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.dz1', 'old_label': '1296.bd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.bd1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247042
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.cl1', '432.bg1', '432.bh1', '432.bi1', '648.dz1'], 'contains': ['2592.h1', '2592.bx1', '2592.by1', '3888.g1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [21241, 36, 15552, 31084], 'label': '31104.fx.1296.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.dz1', 'old_label': '1296.be1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.be1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247043
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.q1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.bd1', '432.bj1', '432.bk1', '648.b1', '648.n1', '648.ec1'], 'contains': ['2592.i1', '2592.n1', '2592.bk1', '2592.fd1', '2592.fw1', '3888.f1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [1, 36, 18144, 10368], 'label': '31104.fx.1296.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cm1', 'old_label': '1296.bf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.bf1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247044
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.bf1', '432.bj1', '432.bl1', '648.c1', '648.o1', '648.ed1'], 'contains': ['2592.j1', '2592.o1', '2592.bl1', '2592.fe1', '2592.fx2', '3888.f1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [20737, 36, 15552, 12384], 'label': '31104.fx.1296.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.co1', 'old_label': '1296.bg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.bg1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247045
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.be1', '432.bj1', '432.bm1', '648.d1', '648.o1', '648.ee1'], 'contains': ['2592.k1', '2592.p1', '2592.bm1', '2592.fe1', '2592.fx1', '3888.f1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [20737, 36, 18144, 12384], 'label': '31104.fx.1296.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cn1', 'old_label': '1296.bh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.bh1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247046
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.bk1', '432.bl1', '432.bm1', '648.e1', '648.p1', '648.ef1'], 'contains': ['2592.l1', '2592.q1', '2592.bj1', '2592.ff1', '2592.gb1', '3888.f1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [20737, 36, 18144, 1728], 'label': '31104.fx.1296.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cp1', 'old_label': '1296.bi1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.bi1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247047
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '48.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.w1', '24.s1', '24.v1', '24.w1'], 'contains': ['96.n1', '144.fr1', '144.fs1', '144.ft1', '144.fu1', '192.t1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [1, 18576, 10368, 12096, 2592, 5712, 22752], 'label': '31104.fx.48.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.x1', 'old_label': '48.bb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bb1', 'subgroup_fusion': None, 'weyl_group': '2592.jb'}
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id: 186247048
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.v1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.bg1', '432.bn1', '432.bo1', '648.b1', '648.r1', '648.ec1'], 'contains': ['2592.i1', '2592.bp1', '2592.bq1', '3888.g1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [15625, 36, 18144, 10368], 'label': '31104.fx.1296.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cm1', 'old_label': '1296.bj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.bj1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247049
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.bi1', '432.bo1', '432.bp1', '648.c1', '648.t1', '648.ed1'], 'contains': ['2592.j1', '2592.br1', '2592.bt1', '3888.g1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5689, 36, 15552, 12384], 'label': '31104.fx.1296.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.co1', 'old_label': '1296.bk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.bk1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247050
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.bh1', '432.bo1', '432.bq1', '648.d1', '648.u1', '648.ee1'], 'contains': ['2592.k1', '2592.bs1', '2592.bu1', '3888.g1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [23401, 36, 18144, 12384], 'label': '31104.fx.1296.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cn1', 'old_label': '1296.bl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.bl1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247051
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.bn1', '432.bp1', '432.bq1', '648.e1', '648.w1', '648.ef1'], 'contains': ['2592.l1', '2592.bv1', '2592.bw1', '3888.g1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5257, 36, 18144, 1728], 'label': '31104.fx.1296.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cp1', 'old_label': '1296.bm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.bm1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247052
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.q1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.br1', '432.bx1', '648.f1', '648.n1', '648.eg1'], 'contains': ['2592.n1', '2592.u1', '2592.bk1', '2592.fw1', '2592.fy1', '3888.h1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [1, 2628, 18144, 10368], 'label': '31104.fx.1296.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cm1', 'old_label': '1296.bn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.bn1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 186247053
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.br1', '432.by1', '648.g1', '648.o1', '648.eh1'], 'contains': ['2592.o1', '2592.v1', '2592.bl1', '2592.fx1', '2592.fz1', '3888.h1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [20737, 2628, 15552, 12384], 'label': '31104.fx.1296.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.co1', 'old_label': '1296.bo1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.bo1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247054
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.br1', '432.bz1', '648.h1', '648.o1', '648.ei1'], 'contains': ['2592.p1', '2592.w1', '2592.bm1', '2592.fx2', '2592.fz1', '3888.h1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [20737, 15588, 18144, 12384], 'label': '31104.fx.1296.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cn1', 'old_label': '1296.bp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.bp1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247055
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.bs1', '432.bu1', '432.ca1', '648.f1', '648.bp1', '648.ec1'], 'contains': ['2592.n1', '2592.z1', '2592.bq1', '3888.i1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [5257, 18252, 18144, 22752], 'label': '31104.fx.1296.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cm1', 'old_label': '1296.bq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.bq1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247056
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.bs1', '432.bw1', '432.cb1', '648.g1', '648.bq2', '648.ed1'], 'contains': ['2592.o1', '2592.ba1', '2592.bt1', '3888.i1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5689, 18684, 15552, 12384], 'label': '31104.fx.1296.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.co1', 'old_label': '1296.br1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.br1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247057
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.bs1', '432.bv1', '432.cc1', '648.h1', '648.bq1', '648.ee1'], 'contains': ['2592.p1', '2592.bb1', '2592.bu1', '3888.i1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [23401, 18252, 18144, 12384], 'label': '31104.fx.1296.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cn1', 'old_label': '1296.bs1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.bs1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247058
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '48.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1', '16.d1'], 'contains': ['96.o1', '96.p1', '96.w1', '96.z1', '96.ba1', '144.fx1', '144.fz1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [1, 22752, 16080, 24198, 10368, 36, 18580], 'label': '31104.fx.48.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bc1', 'old_label': '48.bc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bc1', 'subgroup_fusion': None, 'weyl_group': '648.734'}
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id: 186247059
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.bt1', '432.cd1', '648.b1', '648.bp1', '648.eg1'], 'contains': ['2592.n1', '2592.be1', '2592.bq1', '3888.j1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [15625, 15660, 18144, 10368], 'label': '31104.fx.1296.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cm1', 'old_label': '1296.bt1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.bt1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247060
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.bt1', '432.ce1', '648.c1', '648.bq2', '648.eh1'], 'contains': ['2592.o1', '2592.bf1', '2592.bt1', '3888.j1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5689, 16092, 15552, 12384], 'label': '31104.fx.1296.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.co1', 'old_label': '1296.bu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.bu1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247061
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.bt1', '432.cf1', '648.d1', '648.bq1', '648.ei1'], 'contains': ['2592.p1', '2592.bg1', '2592.bu1', '3888.j1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [23401, 2700, 18144, 12384], 'label': '31104.fx.1296.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cn1', 'old_label': '1296.bv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.bv1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247062
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.cx1', '432.bu1', '432.bv1', '432.bw1', '648.dz1'], 'contains': ['2592.r1', '2592.t1', '2592.by1', '3888.i1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [21241, 18684, 15552, 31084], 'label': '31104.fx.1296.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.dz1', 'old_label': '1296.bw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.bw1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247063
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.bx1', '432.by1', '432.bz1', '648.i1', '648.p1', '648.ek1'], 'contains': ['2592.q1', '2592.x2', '2592.bj1', '2592.gb1', '2592.gc1', '3888.h1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [20737, 2628, 18144, 1728], 'label': '31104.fx.1296.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cp1', 'old_label': '1296.bx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.bx1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247064
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ca1', '432.cb1', '432.cc1', '648.i1', '648.bt1', '648.ef1'], 'contains': ['2592.q1', '2592.bc1', '2592.bw1', '3888.i1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5257, 18252, 18144, 1728], 'label': '31104.fx.1296.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cp1', 'old_label': '1296.by1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.by1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247065
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.cd1', '432.ce1', '432.cf1', '648.e1', '648.bt1', '648.ek1'], 'contains': ['2592.q1', '2592.bh2', '2592.bw1', '3888.j1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5257, 15660, 18144, 1728], 'label': '31104.fx.1296.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cp1', 'old_label': '1296.bz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.bz1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247066
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.cz1', '432.cg1', '432.ch1', '432.ci1', '648.dz1'], 'contains': ['2592.t1', '2592.bn1', '2592.bx1', '3888.l1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [20737, 18684, 15552, 12940], 'label': '31104.fx.1296.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.dz1', 'old_label': '1296.ca1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ca1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247067
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.v1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.cj1', '432.ck1', '648.f1', '648.r1', '648.eg1'], 'contains': ['2592.u1', '2592.bp1', '2592.bq1', '3888.k1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [5257, 2628, 18144, 22752], 'label': '31104.fx.1296.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cm1', 'old_label': '1296.cb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.cb1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247068
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ck1', '432.cl1', '648.g1', '648.t1', '648.eh1'], 'contains': ['2592.v1', '2592.br1', '2592.bt1', '3888.k1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5689, 2628, 15552, 12384], 'label': '31104.fx.1296.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.co1', 'old_label': '1296.cc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.cc1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247069
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '48.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.x1', '16.d1'], 'contains': ['96.q1', '96.r1', '96.t1', '96.u1', '96.v1', '96.y1', '96.bb1', '144.fy1', '144.fz1', '144.ga1'], 'core': '576.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [1, 22752, 12096, 6, 10368, 36, 5712], 'label': '31104.fx.48.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bd1', 'old_label': '48.bd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bd1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
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id: 186247070
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ck1', '432.cm1', '648.h1', '648.u1', '648.ei1'], 'contains': ['2592.w1', '2592.bs1', '2592.bu1', '3888.k1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [23401, 15588, 18144, 12384], 'label': '31104.fx.1296.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cn1', 'old_label': '1296.cd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.cd1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247071
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.cj1', '432.cl1', '432.cm1', '648.i1', '648.w1', '648.ek1'], 'contains': ['2592.x2', '2592.bv1', '2592.bw1', '3888.k1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5257, 2628, 18144, 1728], 'label': '31104.fx.1296.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cp1', 'old_label': '1296.ce1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ce1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247072
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.cn1', '432.co1', '432.cp1', '648.i1', '648.bv1', '648.ef1'], 'contains': ['2592.bc1', '2592.bj1', '2592.bv1', '3888.l1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [20737, 18252, 18144, 1728], 'label': '31104.fx.1296.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cp1', 'old_label': '1296.cf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.cf1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247073
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.cg1', '432.cn1', '432.cq1', '648.f1', '648.bw1', '648.ec1'], 'contains': ['2592.z1', '2592.bk1', '2592.bp1', '3888.l1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [20737, 18252, 18144, 22752], 'label': '31104.fx.1296.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cm1', 'old_label': '1296.cg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.cg1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247074
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ci1', '432.co1', '432.cq1', '648.g1', '648.bx1', '648.ed1'], 'contains': ['2592.ba1', '2592.bl1', '2592.br1', '3888.l1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [20737, 18684, 15552, 12384], 'label': '31104.fx.1296.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.co1', 'old_label': '1296.ch1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ch1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247075
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ch1', '432.cp1', '432.cq1', '648.h1', '648.by1', '648.ee1'], 'contains': ['2592.bb1', '2592.bm1', '2592.bs1', '3888.l1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [20737, 18252, 18144, 12384], 'label': '31104.fx.1296.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cn1', 'old_label': '1296.ci1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ci1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247076
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.cr1', '432.cs1', '432.ct1', '648.e1', '648.bv1', '648.ek1'], 'contains': ['2592.bh2', '2592.bj1', '2592.bv1', '3888.m1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [20737, 15660, 18144, 1728], 'label': '31104.fx.1296.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cp1', 'old_label': '1296.cj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.cj1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247077
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.cr1', '432.cu1', '648.b1', '648.bw1', '648.eg1'], 'contains': ['2592.be1', '2592.bk1', '2592.bp1', '3888.m1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [1, 15660, 18144, 10368], 'label': '31104.fx.1296.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cm1', 'old_label': '1296.ck1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ck1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247078
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.cs1', '432.cu1', '648.c1', '648.bx1', '648.eh1'], 'contains': ['2592.bf1', '2592.bl1', '2592.br1', '3888.m1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [20737, 16092, 15552, 12384], 'label': '31104.fx.1296.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.co1', 'old_label': '1296.cl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.cl1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247079
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ct1', '432.cu1', '648.d1', '648.by1', '648.ei1'], 'contains': ['2592.bg1', '2592.bm1', '2592.bs1', '3888.m1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [20737, 2700, 18144, 12384], 'label': '31104.fx.1296.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cn1', 'old_label': '1296.cm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.cm1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247080
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.a1', '27.d1'], 'contains': ['108.j1', '108.s1', '108.t1', '108.z1', '108.ba1', '108.bv1', '108.bw1', '162.a1', '162.b1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [21265, 15984, 18576, 15558, 18648, 10368, 12096, 36], 'label': '31104.fx.54.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '54.a1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.a1', 'subgroup_fusion': None, 'weyl_group': '576.7160'}
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id: 186247081
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.bd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.cv1', '432.cw1', '432.cx1', '648.j1', '648.m1', '648.n1', '648.q1', '648.r1', '648.cn1', '648.em1'], 'contains': ['2592.i1', '2592.u1', '2592.cb1', '2592.ct1', '2592.do1', '3888.n1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [36, 18144, 16056, 10368], 'label': '31104.fx.1296.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '1296.cn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.cn1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247082
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.bd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.cx1', '432.cy1', '432.cz1', '648.o1', '648.s1', '648.t1', '648.u1', '648.co1', '648.en1', '648.eo1'], 'contains': ['2592.j1', '2592.k1', '2592.v1', '2592.w1', '2592.cc1', '2592.cu1', '2592.dp1', '3888.n1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [36, 16056, 18144, 12384], 'label': '31104.fx.1296.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.w1', 'old_label': '1296.co1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.co1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247083
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.cv1', '432.cy1', '648.k1', '648.p1', '648.v1', '648.w1', '648.cp1', '648.ep1'], 'contains': ['2592.l1', '2592.x2', '2592.cd1', '2592.cv1', '2592.dq1', '3888.n1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [36, 18648, 18576, 12096], 'label': '31104.fx.1296.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '1296.cp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.cp1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247084
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.cw1', '432.cy1', '432.cz1', '648.cr1', '648.ep1', '648.eq1'], 'contains': ['2592.l1', '2592.m1', '2592.x1', '2592.y2', '2592.ce1', '2592.cx1', '2592.ds1', '3888.n1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [36, 18144, 18648, 12096], 'label': '31104.fx.1296.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.di1', 'old_label': '1296.cq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.cq1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247085
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.cv1', '432.cw1', '432.cz1', '648.l1', '648.cq1', '648.eq1'], 'contains': ['2592.m1', '2592.y1', '2592.cf1', '2592.cw1', '2592.dr1', '3888.n1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [36, 15552, 2592, 12096], 'label': '31104.fx.1296.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.t1', 'old_label': '1296.cr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.cr1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247086
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.nh1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.da1', '432.dd1', '648.j1', '648.x1', '648.y1', '648.ba1', '648.bj1', '648.bk1', '648.cs1'], 'contains': ['2592.cb1', '2592.cy1', '2592.eb1', '3888.o1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [17371, 18648, 10368, 18576], 'label': '31104.fx.1296.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '1296.cs1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.cs1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247087
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.nu1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.da1', '432.db1', '648.k1', '648.z1', '648.bb1', '648.bd1', '648.be1', '648.bf1', '648.ct1'], 'contains': ['2592.cd1', '2592.cz1', '2592.ej1', '3888.o1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [12138, 18648, 12096, 18576], 'label': '31104.fx.1296.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '1296.ct1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ct1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247088
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.gc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.da1', '432.dc1', '648.l1', '648.bc1', '648.cu1'], 'contains': ['2592.cf1', '2592.da1', '2592.ek1', '3888.o1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [17371, 15552, 12096, 2592], 'label': '31104.fx.1296.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.j1', 'old_label': '1296.cu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.cu1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247089
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.nh1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.db1', '432.dc1', '432.dd1', '648.m1', '648.bg1', '648.bh1', '648.bi1', '648.bj1', '648.bk1', '648.cv1'], 'contains': ['2592.cb1', '2592.db1', '2592.ec1', '3888.o1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [12138, 18144, 16056, 10368], 'label': '31104.fx.1296.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '1296.cv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.cv1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247090
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.kw1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.de1', '432.df1', '432.dg1', '648.m1', '648.x1', '648.y1', '648.bg1', '648.bl1', '648.bm1', '648.cw1'], 'contains': ['2592.cb1', '2592.dc1', '2592.ee1', '3888.p1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [26047, 18648, 22752, 18576], 'label': '31104.fx.1296.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '1296.cw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.cw1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247091
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.a1', '27.d1'], 'contains': ['108.l1', '108.q1', '108.t1', '108.bg1', '108.bh1', '108.bp1', '108.bq1', '162.b1', '162.d1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [21265, 15984, 18576, 6, 18648, 10368, 12096, 36], 'label': '31104.fx.54.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '54.b1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.b1', 'subgroup_fusion': None, 'weyl_group': '576.7160'}
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id: 186247092
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.kw1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.dg1', '432.dh1', '648.j1', '648.ba1', '648.bh1', '648.bi1', '648.bl1', '648.bm1', '648.cx1'], 'contains': ['2592.cb1', '2592.dd1', '2592.ef1', '3888.p1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26047, 18648, 18576, 10368], 'label': '31104.fx.1296.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '1296.cx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.cx1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247093
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.lg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.de1', '432.dh1', '648.k1', '648.z1', '648.bb1', '648.bd1', '648.bn1', '648.bo1', '648.cy1'], 'contains': ['2592.cd1', '2592.de1', '2592.em1', '3888.p1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [6, 18648, 18576, 12096], 'label': '31104.fx.1296.cy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '1296.cy1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.cy1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247094
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ep1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.df1', '432.dh1', '648.l1', '648.bc1', '648.cz1'], 'contains': ['2592.cf1', '2592.df1', '2592.en1', '3888.p1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [6, 18144, 16056, 12096], 'label': '31104.fx.1296.cz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.k1', 'old_label': '1296.cz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.cz1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247095
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.di1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.di1', '432.dj1', '648.n1', '648.x1', '648.bh1', '648.bp1', '648.br1', '648.da1', '648.er1'], 'contains': ['2592.n1', '2592.cb1', '2592.dg1', '3888.q1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [10405, 15552, 2592, 10368], 'label': '31104.fx.1296.da1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '1296.da1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.da1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
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id: 186247096
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.di1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.di1', '432.dk1', '648.o1', '648.bq1', '648.bq2', '648.bs1', '648.db1', '648.es1', '648.et1'], 'contains': ['2592.o1', '2592.p1', '2592.cc1', '2592.dh1', '3888.q1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [10405, 18144, 15552, 12384], 'label': '31104.fx.1296.db1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bd1', 'old_label': '1296.db1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.db1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247097
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.dx1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.dj1', '432.dk1', '648.p1', '648.z1', '648.bt1', '648.bu1', '648.dc1', '648.eu1'], 'contains': ['2592.q1', '2592.cd1', '2592.di1', '3888.q1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [10405, 18144, 2592, 1728], 'label': '31104.fx.1296.dc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '1296.dc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.dc1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
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id: 186247098
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.dl1', '432.dm1', '432.dn1', '648.bp1', '648.bw1', '648.bz1', '648.ca1', '648.dd1', '648.em1', '648.ey1'], 'contains': ['2592.u1', '2592.z1', '2592.be1', '2592.cb1', '2592.dj1', '3888.r1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [15588, 18144, 16056, 22752], 'label': '31104.fx.1296.dd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.v1', 'old_label': '1296.dd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.dd1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247099
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.dn1', '432.do1', '432.dp1', '648.bq1', '648.by1', '648.cb1', '648.cc1', '648.de1', '648.en1', '648.fa1'], 'contains': ['2592.v1', '2592.bb1', '2592.bg1', '2592.cc1', '2592.dk2', '3888.r1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [16020, 16056, 18144, 12384], 'label': '31104.fx.1296.de1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.w1', 'old_label': '1296.de1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.de1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247100
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.de2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.dn1', '432.do2', '432.dp2', '648.bq2', '648.bx1', '648.cb2', '648.cd1', '648.de1', '648.eo1', '648.ez1'], 'contains': ['2592.w1', '2592.ba1', '2592.bf1', '2592.cc1', '2592.dk1', '3888.r1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [15588, 16056, 18144, 12384], 'label': '31104.fx.1296.de2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.w1', 'old_label': '1296.de2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.de2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247101
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.dl1', '432.do1', '432.do2', '648.bt1', '648.bv1', '648.ce1', '648.cf1', '648.df1', '648.ep1', '648.fb1'], 'contains': ['2592.x1', '2592.bc1', '2592.bh2', '2592.cd1', '2592.dl1', '3888.r1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [18180, 18648, 18576, 12096], 'label': '31104.fx.1296.df1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '1296.df1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.df1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247102
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.a1', '27.e1'], 'contains': ['108.m1', '108.u1', '108.v1', '108.bi1', '108.bj1', '108.br1', '108.bs1', '162.a1', '162.d1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [21265, 15984, 18576, 24198, 18648, 10368, 22752, 36], 'label': '31104.fx.54.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '54.c1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.c1', 'subgroup_fusion': None, 'weyl_group': '576.7160'}
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id: 186247103
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.dm1', '432.do1', '432.dp2', '648.dh1', '648.ep1', '648.fc1'], 'contains': ['2592.x1', '2592.x2', '2592.bd1', '2592.bi2', '2592.ce1', '2592.dn2', '2592.dn3', '3888.r1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [18612, 18144, 18648, 12096], 'label': '31104.fx.1296.dg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.di1', 'old_label': '1296.dg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.dg1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247104
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.dg2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.dm1', '432.do2', '432.dp1', '648.dh1', '648.eq1', '648.fb1'], 'contains': ['2592.y1', '2592.bc1', '2592.bh1', '2592.ce1', '2592.dn1', '3888.r1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [2628, 18144, 18648, 12096], 'label': '31104.fx.1296.dg2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.di1', 'old_label': '1296.dg2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.dg2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247105
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.dl1', '432.dm1', '432.dp1', '432.dp2', '648.dg1', '648.eq1', '648.fc1'], 'contains': ['2592.y1', '2592.y2', '2592.bd1', '2592.bi1', '2592.cf1', '2592.dm1', '2592.dm2', '3888.r1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [18684, 15552, 2592, 12096], 'label': '31104.fx.1296.dh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.di1', 'old_label': '1296.dh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.dh1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247106
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.dq1', '432.dr1', '432.ds1', '648.ba1', '648.bg1', '648.br1', '648.ch1', '648.cj1', '648.cn1', '648.ey1'], 'contains': ['2592.be1', '2592.cb1', '2592.dt1', '2592.dt2', '3888.s1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [468, 18144, 16056, 10368], 'label': '31104.fx.1296.di1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '1296.di1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.di1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247107
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ds1', '432.dt1', '432.du1', '648.bs1', '648.ci1', '648.ck1', '648.cl1', '648.co1', '648.ez1', '648.fa1'], 'contains': ['2592.bf1', '2592.bg1', '2592.cc1', '2592.du1', '3888.s1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [468, 16056, 18144, 12384], 'label': '31104.fx.1296.dj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.w1', 'old_label': '1296.dj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.dj1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247108
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.dq1', '432.dt1', '648.bb1', '648.bu1', '648.cg1', '648.cm1', '648.cp1', '648.fb1'], 'contains': ['2592.bh1', '2592.cd1', '2592.dv1', '3888.s1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [2628, 18648, 18576, 12096], 'label': '31104.fx.1296.dk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '1296.dk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.dk1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247109
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.dr1', '432.dt1', '432.du1', '648.cr1', '648.fb1', '648.fc1'], 'contains': ['2592.bh1', '2592.bh2', '2592.bi1', '2592.ce1', '2592.dx1', '3888.s1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [16020, 18144, 18648, 12096], 'label': '31104.fx.1296.dl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.di1', 'old_label': '1296.dl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.dl1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247110
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.dq1', '432.dr1', '432.du1', '648.bc1', '648.cq1', '648.fc1'], 'contains': ['2592.bi1', '2592.bi2', '2592.cf1', '2592.dw1', '2592.dw2', '3888.s1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [18612, 15552, 2592, 12096], 'label': '31104.fx.1296.dm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.t1', 'old_label': '1296.dm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.dm1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247111
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.dn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.dv1', '432.dw1', '648.p1', '648.be1', '648.bn1', '648.bv1', '648.cg1', '648.di1', '648.fd1'], 'contains': ['2592.bj1', '2592.cd1', '2592.dy1', '3888.t1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1, 15552, 2592, 1728], 'label': '31104.fx.1296.dn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '1296.dn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.dn1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 186247112
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.dc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.dv1', '432.dx1', '648.n1', '648.bj1', '648.bl1', '648.bw1', '648.ch1', '648.dj1', '648.fe1'], 'contains': ['2592.bk1', '2592.cb1', '2592.dz1', '3888.t1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1, 15552, 2592, 22752], 'label': '31104.fx.1296.do1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '1296.do1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.do1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
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id: 186247113
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '6.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1', '3.a1'], 'contains': ['12.e1', '12.o1', '18.bh1', '18.bi1', '18.bj1', '96.ba1'], 'core': '12.e1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 18144, 22752, 10368, 15552, 6, 5712, 18576, 16056, 76], 'label': '31104.fx.6.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.m1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.m1', 'subgroup_fusion': None, 'weyl_group': '10368.fj'}
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id: 186247114
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.b1', '27.d1'], 'contains': ['108.b1', '108.c1', '108.f1', '108.g1', '108.j1', '108.l1', '108.o1', '108.x1', '108.bc1', '108.bk1', '108.bx1', '108.gf1', '108.gh1', '108.gi1', '108.gj1', '108.gl1', '108.gn1', '108.go1', '108.gp1', '162.c1', '162.e1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [5713, 2592, 18576, 6, 16056, 10368, 12096, 36], 'label': '31104.fx.54.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '54.d1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.d1', 'subgroup_fusion': None, 'weyl_group': '576.7160'}
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id: 186247115
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.dc1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.dw1', '432.dx1', '648.o1', '648.bx1', '648.by1', '648.ci1', '648.dk1', '648.ff1', '648.fg1'], 'contains': ['2592.bl1', '2592.bm1', '2592.cc1', '2592.ea1', '3888.t1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1, 18144, 15552, 12384], 'label': '31104.fx.1296.dp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '1296.dp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.dp1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247116
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ec1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.dy1', '432.ec1', '648.q1', '648.y1', '648.bi1', '648.bz1', '648.ch1', '648.da1', '648.fj1'], 'contains': ['2592.cb1', '2592.ed1', '3888.u1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [10837, 18144, 10368, 2592], 'label': '31104.fx.1296.dq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '1296.dq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.dq1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
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id: 186247117
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ed1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.dz1', '432.ed1', '648.r1', '648.bw1', '648.ca1', '648.cj1', '648.dn1', '648.er1', '648.fj1'], 'contains': ['2592.bp1', '2592.cb1', '3888.v1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26461, 2592, 22752, 15552], 'label': '31104.fx.1296.dr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bd1', 'old_label': '1296.dr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.dr1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247118
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.dz1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.ea1', '432.ee1', '648.q1', '648.bk1', '648.bm1', '648.br1', '648.ca1', '648.dj1', '648.fk1'], 'contains': ['2592.cb1', '2592.eg1', '3888.w1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [433, 15552, 2592, 22752], 'label': '31104.fx.1296.ds1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '1296.ds1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ds1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
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id: 186247119
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.ea1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.eb1', '432.ef1', '648.r1', '648.bp1', '648.bz1', '648.cj1', '648.dq1', '648.fe1', '648.fk1'], 'contains': ['2592.bq1', '2592.cb1', '3888.x1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [16057, 2592, 15552, 22752], 'label': '31104.fx.1296.dt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.be1', 'old_label': '1296.dt1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.dt1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247120
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ec1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ec1', '432.eg1', '648.s1', '648.cb1', '648.cb2', '648.ci1', '648.db1', '648.fl1', '648.fm1'], 'contains': ['2592.cc1', '2592.eh1', '3888.u1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [28981, 15552, 12384, 2592], 'label': '31104.fx.1296.du1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bd1', 'old_label': '1296.du1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.du1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247121
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.dv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ed1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ed1', '432.eh1', '648.t1', '648.bx1', '648.cc1', '648.ck1', '648.dr1', '648.et1', '648.fl1'], 'contains': ['2592.br1', '2592.cc1', '3888.v1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [26461, 18144, 12384, 15552], 'label': '31104.fx.1296.dv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bd1', 'old_label': '1296.dv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.dv1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247122
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ed1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ed1', '432.ei1', '648.u1', '648.by1', '648.cd1', '648.cl1', '648.dr1', '648.es1', '648.fm1'], 'contains': ['2592.bs1', '2592.cc1', '3888.v1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [13069, 15552, 12384, 18144], 'label': '31104.fx.1296.dw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bd1', 'old_label': '1296.dw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.dw1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247123
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.dx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.dz1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ee1', '432.ej1', '648.s1', '648.bs1', '648.cc1', '648.cd1', '648.dk1', '648.fn1', '648.fo1'], 'contains': ['2592.cc1', '2592.ei1', '3888.w1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [18577, 15552, 2592, 12384], 'label': '31104.fx.1296.dx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '1296.dx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.dx1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247124
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.ea1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ef1', '432.ek1', '648.t1', '648.bq2', '648.cb1', '648.cl1', '648.ds1', '648.fg1', '648.fn1'], 'contains': ['2592.bt1', '2592.cc1', '3888.x1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [16057, 18144, 15552, 12384], 'label': '31104.fx.1296.dy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '1296.dy1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.dy1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247125
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1', '27.e1'], 'contains': ['108.d1', '108.e1', '108.h1', '108.i1', '108.m1', '108.n1', '108.bb1', '108.bl1', '108.bt1', '108.gg1', '108.gk1', '108.gm1', '108.gq1', '162.e1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [5713, 2592, 18576, 24198, 16056, 10368, 22752, 36], 'label': '31104.fx.54.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '54.e1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.e1', 'subgroup_fusion': None, 'weyl_group': '576.7160'}
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id: 186247126
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.dy2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.ea1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ef1', '432.ek2', '648.u1', '648.bq1', '648.cb2', '648.ck1', '648.ds1', '648.ff1', '648.fo1'], 'contains': ['2592.bu1', '2592.cc1', '3888.x1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [2665, 15552, 18144, 12384], 'label': '31104.fx.1296.dy2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '1296.dy2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.dy2', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247127
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ee1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.dy1', '432.eg1', '648.v1', '648.bd1', '648.ce1', '648.cg1', '648.dc1', '648.fp1'], 'contains': ['2592.cd1', '2592.el1', '3888.u1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [10837, 15552, 2592, 1728], 'label': '31104.fx.1296.dz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '1296.dz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.dz1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
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id: 186247128
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ef1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.dz1', '432.eh1', '432.ei1', '648.w1', '648.bv1', '648.cf1', '648.cm1', '648.dv1', '648.eu1', '648.fp1'], 'contains': ['2592.bv1', '2592.cd1', '3888.v1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [26461, 2592, 15552, 1728], 'label': '31104.fx.1296.ea1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '1296.ea1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ea1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247129
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.eb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.eb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ea1', '432.ej1', '648.v1', '648.bf1', '648.bo1', '648.bu1', '648.cf1', '648.di1', '648.fq1'], 'contains': ['2592.cd1', '2592.eo1', '3888.w1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [433, 15552, 1728, 2592], 'label': '31104.fx.1296.eb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '1296.eb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.eb1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 186247130
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ec1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.ec1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.eb1', '432.ek1', '432.ek2', '648.w1', '648.bt1', '648.ce1', '648.cm1', '648.dy1', '648.fd1', '648.fq1'], 'contains': ['2592.bw1', '2592.cd1', '3888.x1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [16057, 2592, 1728, 15552], 'label': '31104.fx.1296.ec1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '1296.ec1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ec1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 186247131
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ed1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.el1', '432.em1', '432.en1', '648.a1', '648.cn1', '648.cs1', '648.cv1', '648.cw1', '648.cx1', '648.da1', '648.dd1', '648.dj1', '648.dl1', '648.dm1', '648.dn1', '648.do1', '648.dp1', '648.dq1'], 'contains': ['2592.a1', '2592.cb1', '2592.ep1', '2592.ep2', '3888.y1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [18576, 18144, 16056, 10368], 'label': '31104.fx.1296.ed1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '1296.ed1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ed1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247132
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ee1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.en1', '432.eo1', '432.ep1', '648.co1', '648.db1', '648.de1', '648.dk1', '648.dr1', '648.ds1', '648.fv1'], 'contains': ['2592.b1', '2592.c1', '2592.cc1', '2592.eq1', '3888.y1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [18576, 16056, 18144, 12384], 'label': '31104.fx.1296.ee1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '1296.ee1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ee1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247133
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ef1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.em1', '432.eo1', '648.cp1', '648.ct1', '648.cy1', '648.dc1', '648.df1', '648.di1', '648.dt1', '648.dv1', '648.dw1', '648.dy1', '648.fw1'], 'contains': ['2592.e1', '2592.cd1', '2592.er1', '3888.y1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [16056, 2592, 18576, 12096], 'label': '31104.fx.1296.ef1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '1296.ef1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ef1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247134
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.eg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.el1', '432.em1', '432.ep1', '648.cq1', '648.cu1', '648.cz1', '648.dg1', '648.du1', '648.dx1', '648.fw1'], 'contains': ['2592.d1', '2592.g1', '2592.cf1', '2592.er1', '2592.es1', '3888.y1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [18144, 16056, 18576, 12096], 'label': '31104.fx.1296.eg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.s1', 'old_label': '1296.eg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.eg1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247135
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.eh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.el1', '432.eo1', '432.ep1', '648.cr1', '648.dh1', '648.fw1'], 'contains': ['2592.e1', '2592.f1', '2592.g1', '2592.ce1', '2592.es1', '3888.y1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [15552, 16056, 15984, 12096], 'label': '31104.fx.1296.eh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1', 'old_label': '1296.eh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.eh1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247136
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1', '27.e1'], 'contains': ['108.n1', '108.u1', '108.bz1', '108.cj1', '108.ck1', '162.f1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [5713, 15984, 18576, 8646, 18648, 10368, 22752, 36], 'label': '31104.fx.54.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '54.f1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.f1', 'subgroup_fusion': None, 'weyl_group': '576.7160'}
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id: 186247137
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ei1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.de1', '432.eq1', '432.er1', '432.ev1', '432.ew1', '648.dz1'], 'contains': ['2592.h1', '2592.t1', '2592.ck1', '3888.z1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [36, 3096, 15552, 12940], 'label': '31104.fx.1296.ei1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ea1', 'old_label': '1296.ei1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ei1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247138
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.ej1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.eq1', '432.es1', '432.ex1', '432.ey1', '648.ea1', '648.el1'], 'contains': ['2592.cl1', '3888.z1', '5184.o1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [36, 12940, 72, 18144], 'label': '31104.fx.1296.ej1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.p1', 'old_label': '1296.ej1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ej1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186247139
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.df1', '432.eq1', '432.et1', '432.eu1', '432.ez1', '432.fa1', '648.eb1'], 'contains': ['2592.cm1', '3888.z1', '5184.p1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [36, 12460, 18648, 15552], 'label': '31104.fx.1296.ek1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ea1', 'old_label': '1296.ek1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ek1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186247140
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.el1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.fx1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.er1', '432.es1', '432.et1', '432.eu1', '432.fb1', '432.fc1', '648.ec1', '648.em1'], 'contains': ['2592.i1', '2592.z1', '2592.cg1', '3888.z1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [36, 3096, 15552, 10368], 'label': '31104.fx.1296.el1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '1296.el1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.el1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186247141
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.em1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.fx1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ew1', '432.ex1', '432.ez1', '432.fc1', '432.fd1', '648.ed1', '648.eo1'], 'contains': ['2592.j1', '2592.ba1', '2592.ch1', '3888.z1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [36, 3096, 15552, 12384], 'label': '31104.fx.1296.em1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1', 'old_label': '1296.em1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.em1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186247142
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.en1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.fx1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ev1', '432.ey1', '432.fa1', '432.fc1', '432.fe1', '648.ee1', '648.en1'], 'contains': ['2592.k1', '2592.bb1', '2592.ci1', '3888.z1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [36, 18216, 18144, 12384], 'label': '31104.fx.1296.en1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1', 'old_label': '1296.en1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.en1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186247143
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.eo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.fb1', '432.fd1', '432.fe1', '648.ef1', '648.ep1', '648.eq1'], 'contains': ['2592.l1', '2592.m1', '2592.bc1', '2592.bd1', '2592.cj1', '3888.z1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [36, 15552, 18648, 12096], 'label': '31104.fx.1296.eo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '1296.eo1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.eo1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247144
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ep1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.ff1', '432.fg1', '432.fh1', '432.fi1', '432.fj1', '432.fk1', '432.fl1', '432.fm1', '432.fn1', '432.fn2', '648.ec1', '648.eg1', '648.er1'], 'contains': ['2592.n1', '2592.bp1', '2592.cg1', '3888.ba1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [10405, 3096, 10368, 15552], 'label': '31104.fx.1296.ep1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cr1', 'old_label': '1296.ep1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ep1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247145
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.eq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ff1', '432.fo1', '432.fr1', '432.fs1', '432.fu1', '432.fw1', '432.fy1', '432.ga1', '648.ed1', '648.eh1', '648.et1'], 'contains': ['2592.o1', '2592.br1', '2592.ch1', '3888.ba1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [10405, 3096, 12384, 15552], 'label': '31104.fx.1296.eq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cr1', 'old_label': '1296.eq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.eq1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247146
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.er1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ff1', '432.fp1', '432.fq1', '432.ft1', '432.fv1', '432.fx1', '432.fz1', '432.gb1', '648.ee1', '648.ei1', '648.es1'], 'contains': ['2592.p1', '2592.bs1', '2592.ci1', '3888.ba1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [10405, 18216, 12384, 18144], 'label': '31104.fx.1296.er1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cr1', 'old_label': '1296.er1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.er1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247147
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.c1', '27.d1'], 'contains': ['108.o1', '108.q1', '108.s1', '108.cc1', '108.cd1', '108.ch1', '108.ci1', '162.f1', '162.g1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [5713, 15984, 18576, 15558, 18648, 10368, 12096, 36], 'label': '31104.fx.54.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '54.g1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.g1', 'subgroup_fusion': None, 'weyl_group': '576.7160'}
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id: 186247148
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.es1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.fg1', '432.fo1', '432.fp1', '648.ef1', '648.ek1', '648.eu1'], 'contains': ['2592.q1', '2592.bv1', '2592.cj1', '3888.ba1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [10405, 3096, 15552, 1728], 'label': '31104.fx.1296.es1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bc1', 'old_label': '1296.es1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.es1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247149
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.et1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.ea1', '432.fh1', '432.fq1', '432.fr1', '432.gc1', '648.dz1'], 'contains': ['2592.r1', '2592.bx1', '2592.ck1', '3888.ba1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [10405, 3096, 15552, 12940], 'label': '31104.fx.1296.et1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bj1', 'old_label': '1296.et1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.et1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247150
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.eu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.fi1', '432.fs1', '432.ft1', '432.gc1', '648.ea1', '648.ej1', '648.ev1'], 'contains': ['2592.cl1', '3888.ba1', '5184.bk1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [10405, 12940, 72, 18144], 'label': '31104.fx.1296.eu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.y1', 'old_label': '1296.eu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.eu1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186247151
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ev1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.ba1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.eb1', '432.fj1', '432.fk1', '432.fu1', '432.fv1', '432.gc1', '648.eb1'], 'contains': ['2592.cm1', '3888.ba1', '5184.bl1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [10405, 16080, 18648, 15552], 'label': '31104.fx.1296.ev1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bl1', 'old_label': '1296.ev1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ev1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186247152
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ew1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.ec1', '432.fl1', '432.fw1', '432.fx1'], 'contains': ['2592.s1', '2592.ca1', '2592.cq1', '3888.ba1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [10405, 18216, 18144, 29404], 'label': '31104.fx.1296.ew1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.bv1', 'old_label': '1296.ew1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ew1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247153
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ex1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.fm1', '432.fy1', '432.fz1', '648.ew1'], 'contains': ['2592.cr1', '3888.ba1', '5184.bm1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [10405, 29404, 3096, 15552], 'label': '31104.fx.1296.ex1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bz1', 'old_label': '1296.ex1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ex1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186247154
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ey1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.ed1', '432.fn1', '432.fn2', '432.ga1', '432.gb1'], 'contains': ['2592.cs1', '3888.ba1', '5184.bn1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [10405, 9168, 18648, 15552], 'label': '31104.fx.1296.ey1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.bx1', 'old_label': '1296.ey1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ey1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186247155
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ez1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.z1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.gd1', '432.ge1', '432.gf1', '648.ej1', '648.el1', '648.ex1'], 'contains': ['2592.cl1', '3888.bb1', '5184.bo1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [468, 12940, 72, 18144], 'label': '31104.fx.1296.ez1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.q1', 'old_label': '1296.ez1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ez1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186247156
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.fa1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.gd1', '432.gg1', '432.gh1', '648.eg1', '648.em1', '648.ey1'], 'contains': ['2592.u1', '2592.be1', '2592.cg1', '3888.bb1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [3060, 3096, 15552, 22752], 'label': '31104.fx.1296.fa1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.u1', 'old_label': '1296.fa1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.fa1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186247157
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.fb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ge1', '432.gh1', '432.gi1', '648.eh1', '648.eo1', '648.fa1'], 'contains': ['2592.v1', '2592.bf1', '2592.ch1', '3888.bb1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [3060, 3096, 15552, 12384], 'label': '31104.fx.1296.fb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '1296.fb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.fb1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186247158
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.d1', '27.d1'], 'contains': ['108.x1', '108.y1', '108.ba1', '108.bn1', '108.bq1', '108.ca1', '108.cd1', '162.h1', '162.i1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [21265, 15984, 18576, 6, 18648, 10368, 12096, 15588], 'label': '31104.fx.54.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '54.h1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.h1', 'subgroup_fusion': None, 'weyl_group': '576.7160'}
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id: 186247159
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.fc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.gf1', '432.gh1', '432.gj1', '432.gj2', '648.ei1', '648.en1', '648.ez1'], 'contains': ['2592.w1', '2592.bg1', '2592.ci1', '3888.bb1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [16020, 18216, 18144, 12384], 'label': '31104.fx.1296.fc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.y1', 'old_label': '1296.fc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.fc1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186247160
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.fd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.gg1', '432.gi1', '432.gj1', '648.ek1', '648.ep1', '648.fc1'], 'contains': ['2592.x2', '2592.y2', '2592.bh2', '2592.bi2', '2592.cj1', '3888.bb1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [18612, 15552, 18648, 12096], 'label': '31104.fx.1296.fd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '1296.fd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.fd1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247161
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.fd2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.gg1', '432.gi1', '432.gj2', '648.eq1', '648.fb1', '648.fc1'], 'contains': ['2592.x1', '2592.y1', '2592.bh1', '2592.bi1', '2592.cj1', '3888.bb1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [2628, 15552, 18648, 12096], 'label': '31104.fx.1296.fd2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.di1', 'old_label': '1296.fd2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.fd2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247162
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.fe1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.gk1', '432.gl1', '432.gm1', '648.ef1', '648.ek1', '648.fd1'], 'contains': ['2592.bj1', '2592.bw1', '2592.cj1', '3888.bc1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1, 3096, 1728, 15552], 'label': '31104.fx.1296.fe1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cp1', 'old_label': '1296.fe1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.fe1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247163
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ff1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.gk1', '432.gn1', '432.go1', '432.gp1', '432.gq1', '432.gr1', '432.gs1', '648.ec1', '648.eg1', '648.fe1'], 'contains': ['2592.bk1', '2592.bq1', '2592.cg1', '3888.bc1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1, 3096, 15552, 10368], 'label': '31104.fx.1296.ff1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cs1', 'old_label': '1296.ff1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ff1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247164
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.fg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.gl1', '432.gs1', '432.gu1', '432.gv1', '432.gx1', '432.gz1', '648.ed1', '648.eh1', '648.fg1'], 'contains': ['2592.bl1', '2592.bt1', '2592.ch1', '3888.bc1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1, 3096, 15552, 12384], 'label': '31104.fx.1296.fg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cu1', 'old_label': '1296.fg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.fg1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247165
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.fh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.gm1', '432.gs1', '432.gt1', '432.gw1', '432.gy1', '432.ha1', '648.ee1', '648.ei1', '648.ff1'], 'contains': ['2592.bm1', '2592.bu1', '2592.ci1', '3888.bc1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1, 18216, 18144, 12384], 'label': '31104.fx.1296.fh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ct1', 'old_label': '1296.fh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.fh1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247166
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.fi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.eh1', '432.gn1', '432.gt1', '432.gu1', '432.hb1', '432.hc1', '432.hf1', '432.hg1', '648.dz1'], 'contains': ['2592.bn1', '2592.by1', '2592.ck1', '3888.bc1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [1, 3096, 15552, 556], 'label': '31104.fx.1296.fi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.dz1', 'old_label': '1296.fi1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.fi1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247167
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.fj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.go1', '432.gv1', '432.gw1', '432.hd1', '432.he1', '432.hf1', '432.hg1', '648.ea1', '648.ej1', '648.fh1'], 'contains': ['2592.cl1', '3888.bc1', '5184.by1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1, 556, 72, 18144], 'label': '31104.fx.1296.fj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.ck1', 'old_label': '1296.fj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.fj1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186247168
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.fk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.ei1', '432.gp1', '432.gq1', '432.gx1', '432.gy1', '432.hb1', '432.hd1', '432.hf1', '432.hh1', '432.hi1', '648.eb1'], 'contains': ['2592.cm1', '3888.bc1', '5184.bz1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [1, 20812, 18648, 15552], 'label': '31104.fx.1296.fk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.eb1', 'old_label': '1296.fk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.fk1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186247169
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.d1', '27.e1'], 'contains': ['108.bb1', '108.bf1', '108.bj1', '108.bo1', '108.bs1', '108.by1', '108.bz1', '162.h1', '162.k1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [21265, 15984, 18576, 8646, 18648, 10368, 22752, 15588], 'label': '31104.fx.54.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '54.i1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.i1', 'subgroup_fusion': None, 'weyl_group': '576.7160'}
-
id: 186247170
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.fl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.ej1', '432.gn1', '432.gt1', '432.gz1', '432.hd1', '432.he1', '432.hh1', '432.hi1', '432.hj1', '432.hj2'], 'contains': ['2592.bo1', '2592.bz1', '2592.cn1', '3888.bc1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [1, 3096, 15552, 10924], 'label': '31104.fx.1296.fl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1296.fl1', 'old_label': '1296.fl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.fl1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247171
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.fm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.go1', '432.gv1', '432.ha1', '432.hb1', '432.hc1', '432.hh1', '432.hi1', '432.hj1', '432.hj2', '648.fi1'], 'contains': ['2592.co1', '3888.bc1', '5184.ca1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [1, 10924, 72, 18144], 'label': '31104.fx.1296.fm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.fi1', 'old_label': '1296.fm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.fm1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186247172
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.fn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.ek1', '432.gp1', '432.gr1', '432.gx1', '432.gy1', '432.hb1', '432.hc1', '432.hd1', '432.he1', '432.hg1', '432.hh1', '432.hj1', '432.hj2'], 'contains': ['2592.cp1', '3888.bc1', '5184.cb1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 2592, 'diagramx': None, 'generators': [1, 76, 18648, 15552], 'label': '31104.fx.1296.fn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1296.fn1', 'old_label': '1296.fn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.fn1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186247173
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.fo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.hk1', '432.hl1', '432.hm1', '432.hn1', '648.a1', '648.em1', '648.er1', '648.ey1', '648.fe1', '648.fj1', '648.fk1'], 'contains': ['2592.a1', '2592.cb1', '2592.cg1', '3888.bd1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [18144, 3096, 15552, 14400], 'label': '31104.fx.1296.fo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '648.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '1296.fo1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.fo1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247174
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.fp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.hn1', '432.ho1', '432.hp1', '432.hs1', '432.ht1', '432.hu1', '432.hv1', '648.en1', '648.es1', '648.ez1', '648.ff1', '648.fl1', '648.fn1', '648.fv1'], 'contains': ['2592.c1', '2592.cc1', '2592.ci1', '3888.bd1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [3024, 18216, 18144, 12384], 'label': '31104.fx.1296.fp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '1296.fp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.fp1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247175
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.fq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.hn1', '432.hq1', '432.hr1', '432.hw1', '648.eo1', '648.et1', '648.fa1', '648.fg1', '648.fm1', '648.fo1', '648.fv1'], 'contains': ['2592.b1', '2592.cc1', '2592.ch1', '3888.bd1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [18144, 3096, 15552, 12384], 'label': '31104.fx.1296.fq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '1296.fq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.fq1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247176
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.fr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.hk1', '432.ho1', '432.hq1', '648.ep1', '648.eu1', '648.fb1', '648.fd1', '648.fp1', '648.fq1', '648.fw1'], 'contains': ['2592.d1', '2592.f1', '2592.cd1', '2592.ce1', '2592.cj1', '3888.bd1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [18144, 18648, 18576, 12096], 'label': '31104.fx.1296.fr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '1296.fr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.fr1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247177
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.fs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.hk1', '432.hp1', '432.hq1', '648.eq1', '648.fc1', '648.fw1'], 'contains': ['2592.e1', '2592.g1', '2592.ce1', '2592.cf1', '2592.cj1', '3888.bd1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [18144, 16056, 2592, 12096], 'label': '31104.fx.1296.fs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1', 'old_label': '1296.fs1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.fs1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247178
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ft1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.fc1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.hl1', '432.hr1', '432.hs1', '648.el1', '648.ev1', '648.ex1', '648.fh1', '648.fr1', '648.fs1', '648.fx1'], 'contains': ['2592.cl1', '3888.bd1', '5184.f1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [16056, 24460, 72, 18144], 'label': '31104.fx.1296.ft1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '1296.ft1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ft1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186247179
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.fu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.df1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.hl1', '432.hr1', '432.ht1', '648.fi1', '648.ft1', '648.fz1'], 'contains': ['2592.co1', '3888.bd1', '5184.g1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [16056, 10924, 72, 18144], 'label': '31104.fx.1296.fu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.de1', 'old_label': '1296.fu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.fu1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186247180
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.d1', '27.d1'], 'contains': ['108.bc1', '108.be1', '108.bh1', '108.bu1', '108.bw1', '108.ca1', '108.cc1', '162.i1', '162.k1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [21265, 15984, 18576, 15558, 18648, 10368, 12096, 15588], 'label': '31104.fx.54.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '54.j1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.j1', 'subgroup_fusion': None, 'weyl_group': '576.7160'}
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id: 186247181
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.fv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.df1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.hm1', '432.hu1', '432.hw1', '648.ew1', '648.fu1', '648.gb1'], 'contains': ['2592.cr1', '3888.bd1', '5184.h1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [16056, 29404, 18648, 15552], 'label': '31104.fx.1296.fv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cp1', 'old_label': '1296.fv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.fv1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186247182
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.fw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.df1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.hm1', '432.hv1', '432.hw1', '648.gb1'], 'contains': ['2592.cr1', '3888.bd1', '5184.i1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [18576, 29404, 18648, 15552], 'label': '31104.fx.1296.fw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.cy1', 'old_label': '1296.fw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.fw1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
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id: 186247183
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.fx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cp1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.hx1', '432.ia1', '648.j1', '648.gd1', '648.gf1', '648.gl1', '648.gm1', '648.ig1', '648.ij1'], 'contains': ['2592.ct1', '2592.cy1', '2592.dd1', '2592.fa1', '2592.fk1', '3888.be1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [29503, 36, 18576, 10368], 'label': '31104.fx.1296.fx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '1296.fx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.fx1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247184
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.fy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cr1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.hx1', '432.hy1', '648.k1', '648.ge1', '648.gg1', '648.gh1', '648.gi1', '648.ih1', '648.ik1'], 'contains': ['2592.cv1', '2592.cz1', '2592.de1', '2592.fb1', '2592.fl1', '3888.be1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [26047, 36, 18576, 12096], 'label': '31104.fx.1296.fy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '1296.fy1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.fy1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 186247185
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.fz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.co1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.hx1', '432.hz1', '648.l1', '648.ii1', '648.ik1'], 'contains': ['2592.cw1', '2592.da1', '2592.df1', '2592.fb1', '2592.fl2', '3888.be1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [6, 36, 16056, 12096], 'label': '31104.fx.1296.fz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.k1', 'old_label': '1296.fz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.fz1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247186
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ga1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cm1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.hy1', '432.hz1', '432.ia1', '648.m1', '648.gj1', '648.gk1', '648.gl1', '648.gm1', '648.il1', '648.im1'], 'contains': ['2592.ct1', '2592.db1', '2592.dc1', '2592.fc1', '2592.fo1', '3888.be1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [19135, 36, 18576, 22752], 'label': '31104.fx.1296.ga1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '1296.ga1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ga1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 186247187
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.gb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.ib1', '432.ic1', '648.n1', '648.gd1', '648.gj1', '648.gl1', '648.gn1', '648.in1', '648.in2'], 'contains': ['2592.ct1', '2592.dg1', '2592.dz1', '2592.fd1', '2592.fy1', '3888.bf1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1, 36, 2592, 10368], 'label': '31104.fx.1296.gb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '1296.gb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.gb1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 186247188
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.gc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ib1', '432.id1', '648.o1', '648.io1'], 'contains': ['2592.cu1', '2592.dh1', '2592.ea1', '2592.fe1', '2592.fz1', '3888.bf1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [20737, 36, 2592, 12384], 'label': '31104.fx.1296.gc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.n1', 'old_label': '1296.gc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.gc1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 186247189
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.gd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ic1', '432.id1', '648.p1', '648.ge1', '648.gh1', '648.go1', '648.ip1'], 'contains': ['2592.cv1', '2592.di1', '2592.dy1', '2592.ff1', '2592.gc1', '3888.bf1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [20737, 36, 2592, 1728], 'label': '31104.fx.1296.gd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '1296.gd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.gd1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247190
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ge1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cs1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.ie1', '432.ii1', '648.j1', '648.gj1', '648.gk1', '648.gn1', '648.gp1', '648.ig1', '648.iq1'], 'contains': ['2592.ct1', '2592.eb1', '2592.ef1', '3888.bg1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [14311, 36, 18576, 10368], 'label': '31104.fx.1296.ge1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '1296.ge1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ge1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247191
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.e1', '27.d1'], 'contains': ['108.y1', '108.z1', '108.be1', '108.bg1', '108.bk1', '108.ce1', '108.ci1', '162.j1', '162.l1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [5713, 15984, 18576, 15558, 18648, 10368, 12096, 15588], 'label': '31104.fx.54.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '54.k1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.k1', 'subgroup_fusion': None, 'weyl_group': '576.7160'}
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id: 186247192
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.gf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cn1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.if1', '432.ig1', '432.ii1', '648.m1', '648.gd1', '648.gf1', '648.gn1', '648.gp1', '648.il1', '648.ir1'], 'contains': ['2592.ct1', '2592.ec1', '2592.ee1', '3888.bg1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [3943, 36, 18576, 22752], 'label': '31104.fx.1296.gf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '1296.gf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.gf1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247193
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.gg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.ih1', '432.ij1', '648.q1', '648.gf1', '648.gk1', '648.gm1', '648.gp1', '648.in1', '648.in2'], 'contains': ['2592.ct1', '2592.ed1', '2592.eg1', '3888.bh1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [15985, 36, 2592, 10368], 'label': '31104.fx.1296.gg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '1296.gg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.gg1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 186247194
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.gh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ij1', '432.ik1', '648.s1', '648.io1'], 'contains': ['2592.cu1', '2592.eh1', '2592.ei1', '3888.bh1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [8209, 36, 2592, 12384], 'label': '31104.fx.1296.gh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.n1', 'old_label': '1296.gh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.gh1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247195
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.gi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.co1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.ie1', '432.if1', '648.k1', '648.ge1', '648.gg1', '648.go1', '648.gq1', '648.ih1', '648.is1'], 'contains': ['2592.cv1', '2592.ej1', '2592.em1', '3888.bg1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [28567, 36, 18576, 12096], 'label': '31104.fx.1296.gi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '1296.gi1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.gi1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 186247196
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.gj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cu1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.ie1', '432.ig1', '648.l1', '648.ii1', '648.it1'], 'contains': ['2592.cw1', '2592.ek1', '2592.en1', '3888.bg1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [18150, 36, 16056, 12096], 'label': '31104.fx.1296.gj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.k1', 'old_label': '1296.gj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.gj1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247197
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.gk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ih1', '432.ik1', '648.v1', '648.gg1', '648.gi1', '648.gq1', '648.ip1'], 'contains': ['2592.cv1', '2592.el1', '2592.eo1', '3888.bh1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [5617, 36, 2592, 1728], 'label': '31104.fx.1296.gk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '1296.gk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.gk1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 186247198
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.gl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.gl1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.il1', '432.iu1', '648.x1', '648.gl1', '648.gr1', '648.gv1', '648.hn1', '648.iu1', '648.jd1'], 'contains': ['2592.cy1', '2592.dc1', '2592.dg1', '2592.fg1', '3888.bi1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [26485, 12138, 18576, 22752], 'label': '31104.fx.1296.gl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '1296.gl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.gl1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 186247199
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.gm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.gm1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.im1', '432.iy1', '648.y1', '648.gm1', '648.gs1', '648.gw1', '648.ho1', '648.iu1', '648.jd1'], 'contains': ['2592.cy1', '2592.dc1', '2592.ed1', '3888.bk1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [29077, 12138, 22752, 18576], 'label': '31104.fx.1296.gm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '1296.gm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.gm1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 186247200
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.gn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.hr1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.il1', '432.iz1', '648.z1', '648.gh1', '648.gt1', '648.gx1', '648.hd1', '648.iy1', '648.je1'], 'contains': ['2592.cz1', '2592.de1', '2592.di1', '2592.fh1', '3888.bi1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26485, 12138, 18576, 12096], 'label': '31104.fx.1296.gn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '1296.gn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.gn1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247201
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.go1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.co1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.in1', '432.ix1', '648.ba1', '648.gv1', '648.gw1', '648.hp1', '648.hq1', '648.ij1', '648.iv1'], 'contains': ['2592.cy1', '2592.dd1', '2592.dt2', '2592.fk1', '3888.bj1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [29503, 2628, 18576, 10368], 'label': '31104.fx.1296.go1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '1296.go1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.go1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247202
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.e1', '27.e1'], 'contains': ['108.bf1', '108.bi1', '108.bl1', '108.cg1', '108.ck1', '162.l1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [5713, 15984, 18576, 8646, 18648, 10368, 22752, 15588], 'label': '31104.fx.54.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '54.l1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.l1', 'subgroup_fusion': None, 'weyl_group': '576.7160'}
-
id: 186247203
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.gp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.co1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.in1', '432.iv1', '648.bb1', '648.gx1', '648.gy1', '648.hd1', '648.he1', '648.ik1', '648.iw1'], 'contains': ['2592.cz1', '2592.de1', '2592.dv1', '2592.fl2', '3888.bj1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [26047, 2628, 18576, 12096], 'label': '31104.fx.1296.gp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '1296.gp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.gp1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247204
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.gq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.co1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.in1', '432.iw1', '648.bc1', '648.ik1', '648.ix1'], 'contains': ['2592.da1', '2592.df1', '2592.dw2', '2592.fl1', '2592.fl2', '3888.bj1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [6, 18612, 16056, 12096], 'label': '31104.fx.1296.gq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.k1', 'old_label': '1296.gq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.gq1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 186247205
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.gr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.hs1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.im1', '432.ja1', '648.bd1', '648.gi1', '648.gu1', '648.gy1', '648.he1', '648.iy1', '648.je1'], 'contains': ['2592.cz1', '2592.de1', '2592.el1', '3888.bk1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [29077, 12138, 18576, 12096], 'label': '31104.fx.1296.gr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '1296.gr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.gr1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247206
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.gs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.gs1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.io1', '432.jb1', '648.x1', '648.gd1', '648.gz1', '648.hp1', '648.hr1', '648.iz1', '648.jd1'], 'contains': ['2592.cy1', '2592.dg1', '2592.ee1', '3888.bl1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [26485, 14802, 22752, 18576], 'label': '31104.fx.1296.gs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '1296.gs1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.gs1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 186247207
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.gt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.hb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.io1', '432.jc1', '648.z1', '648.ge1', '648.ha1', '648.hd1', '648.hf1', '648.ja1', '648.je1'], 'contains': ['2592.cz1', '2592.di1', '2592.em1', '3888.bl1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26485, 14802, 18576, 12096], 'label': '31104.fx.1296.gt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '1296.gt1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.gt1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247208
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.gu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cr1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.ip1', '432.jf1', '648.j1', '648.gr1', '648.gs1', '648.hr1', '648.hs1', '648.iv1', '648.jh1'], 'contains': ['2592.cy1', '2592.do1', '2592.ef1', '3888.bm1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [14311, 18684, 18576, 10368], 'label': '31104.fx.1296.gu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '1296.gu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.gu1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247209
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.gv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.ct1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.ip1', '432.jd1', '648.k1', '648.gt1', '648.gu1', '648.hf1', '648.hg1', '648.iw1', '648.ji2'], 'contains': ['2592.cz1', '2592.dq1', '2592.em1', '3888.bm1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [28567, 108, 18576, 12096], 'label': '31104.fx.1296.gv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '1296.gv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.gv1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247210
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.gw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.ip1', '432.je1', '648.l1', '648.ix1', '648.ji1'], 'contains': ['2592.da1', '2592.dr1', '2592.en1', '3888.bm1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [18150, 18180, 16056, 12096], 'label': '31104.fx.1296.gw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.k1', 'old_label': '1296.gw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.gw1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247211
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.gx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cp1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.iq1', '432.ji1', '648.ba1', '648.gz1', '648.hc1', '648.hn1', '648.ho1', '648.ig1', '648.jh1'], 'contains': ['2592.cy1', '2592.dt1', '2592.ef1', '3888.bn1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [14311, 16092, 18576, 10368], 'label': '31104.fx.1296.gx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '1296.gx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.gx1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247212
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.gy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cn1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.iq1', '432.jg1', '648.bb1', '648.ha1', '648.hb1', '648.hd1', '648.he1', '648.ih1', '648.ji2'], 'contains': ['2592.cz1', '2592.dv1', '2592.em1', '3888.bn1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [28567, 2700, 18576, 12096], 'label': '31104.fx.1296.gy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '1296.gy1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.gy1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247213
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.f1', '27.e1'], 'contains': ['108.bo1', '108.br1', '108.bt1', '108.cg1', '108.cj1', '162.m1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [5713, 15984, 18576, 24198, 18648, 10368, 22752, 15588], 'label': '31104.fx.54.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '54.m1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.m1', 'subgroup_fusion': None, 'weyl_group': '576.7160'}
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id: 186247214
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.gz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.iq1', '432.jh1', '648.bc1', '648.ii1', '648.ji1'], 'contains': ['2592.da1', '2592.dw1', '2592.en1', '3888.bn1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [18150, 468, 16056, 12096], 'label': '31104.fx.1296.gz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.k1', 'old_label': '1296.gz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.gz1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247215
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ha1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.ha1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.ir1', '432.jj1', '648.be1', '648.ge1', '648.gt1', '648.gy1', '648.hb1', '648.jb1', '648.jn1'], 'contains': ['2592.cz1', '2592.dy1', '2592.ej1', '3888.bo1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 14730, 12096, 18576], 'label': '31104.fx.1296.ha1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '1296.ha1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ha1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247216
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.hb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.gt1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.ir1', '432.jk1', '648.bj1', '648.gd1', '648.gr1', '648.gw1', '648.hc1', '648.jc1', '648.jp1'], 'contains': ['2592.cy1', '2592.dz1', '2592.ec1', '3888.bo1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 14730, 18576, 10368], 'label': '31104.fx.1296.hb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '1296.hb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.hb1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247217
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.hc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.hf1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.is1', '432.jn1', '648.bk1', '648.gf1', '648.gs1', '648.gv1', '648.gz1', '648.jc1', '648.jp1'], 'contains': ['2592.cy1', '2592.ec1', '2592.eg1', '3888.bp1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [8305, 14730, 18576, 10368], 'label': '31104.fx.1296.hc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '1296.hc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.hc1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247218
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.hd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.hd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.it1', '432.jo1', '648.y1', '648.gf1', '648.hc1', '648.hq1', '648.hs1', '648.iz1', '648.jd1'], 'contains': ['2592.cy1', '2592.ed1', '2592.ee1', '3888.bq1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [29077, 14802, 22752, 18576], 'label': '31104.fx.1296.hd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '1296.hd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.hd1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247219
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.he1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.he1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.is1', '432.jl1', '648.bf1', '648.gg1', '648.gu1', '648.gx1', '648.ha1', '648.jb1', '648.jn1'], 'contains': ['2592.cz1', '2592.ej1', '2592.eo1', '3888.bp1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [8305, 14730, 12096, 18576], 'label': '31104.fx.1296.he1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '1296.he1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.he1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247220
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.hf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.hc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.it1', '432.jm1', '648.bd1', '648.gg1', '648.hb1', '648.he1', '648.hg1', '648.ja1', '648.je1'], 'contains': ['2592.cz1', '2592.el1', '2592.em1', '3888.bq1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [29077, 14802, 18576, 12096], 'label': '31104.fx.1296.hf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '1296.hf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.hf1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247221
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.hg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.hg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.jp1', '648.be1', '648.gh1', '648.he1', '648.hf1', '648.jn1'], 'contains': ['2592.cz1', '2592.dy1', '2592.fm1', '3888.br1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [5713, 12138, 18576, 12096], 'label': '31104.fx.1296.hg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '1296.hg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.hg1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247222
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.hh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.hh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.jq1', '648.bf1', '648.gi1', '648.hd1', '648.hg1', '648.jn1'], 'contains': ['2592.cz1', '2592.eo1', '3888.bs1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [8305, 12138, 12096, 18576], 'label': '31104.fx.1296.hh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '1296.hh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.hh1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247223
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.hi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cq1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.iv1', '432.iw1', '432.ix1', '648.bg1', '648.hj1', '648.hk1', '648.hn1', '648.ho1', '648.im1', '648.jj1'], 'contains': ['2592.db1', '2592.dc1', '2592.dt1', '2592.fo1', '3888.bj1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [19135, 2628, 18576, 22752], 'label': '31104.fx.1296.hi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '1296.hi1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.hi1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247224
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '6.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.e1', '3.b1'], 'contains': ['12.d1', '12.n1', '12.w1', '18.bj1', '18.bk1', '18.bl1', '18.bm1', '24.w1'], 'core': '12.d1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [5713, 2592, 10368, 22752, 15552, 6, 12096, 18576, 2664, 15628], 'label': '31104.fx.6.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '6.n1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.n1', 'subgroup_fusion': None, 'weyl_group': '10368.je'}
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id: 186247225
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.f1', '27.d1'], 'contains': ['108.bn1', '108.bp1', '108.bu1', '108.bv1', '108.bx1', '108.ce1', '108.ch1', '162.m1', '162.n1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [5713, 15984, 18576, 6, 18648, 10368, 12096, 15588], 'label': '31104.fx.54.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '54.n1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.n1', 'subgroup_fusion': None, 'weyl_group': '576.7160'}
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id: 186247226
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.hj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.hj1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.iu1', '432.iz1', '648.bh1', '648.gl1', '648.hh1', '648.hj1', '648.hp1', '648.jl1', '648.jr1'], 'contains': ['2592.db1', '2592.dd1', '2592.dg1', '2592.fp1', '3888.bi1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26485, 12138, 18576, 10368], 'label': '31104.fx.1296.hj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '1296.hj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.hj1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247227
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.hk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.hk1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.iy1', '432.ja1', '648.bi1', '648.gm1', '648.hi1', '648.hk1', '648.hq1', '648.jl1', '648.jr1'], 'contains': ['2592.db1', '2592.dd1', '2592.ed1', '3888.bk1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [29077, 12138, 18576, 10368], 'label': '31104.fx.1296.hk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '1296.hk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.hk1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247228
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.hl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.hz1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.jb1', '432.jc1', '648.bh1', '648.gj1', '648.hl1', '648.hn1', '648.hr1', '648.jm1', '648.jr1'], 'contains': ['2592.db1', '2592.dg1', '2592.ef1', '3888.bl1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26485, 14802, 18576, 10368], 'label': '31104.fx.1296.hl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '1296.hl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.hl1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247229
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.hm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cr1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.jd1', '432.je1', '432.jf1', '648.m1', '648.hh1', '648.hi1', '648.hr1', '648.hs1', '648.jj1', '648.js1'], 'contains': ['2592.db1', '2592.do1', '2592.ee1', '3888.bm1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [3943, 18684, 18576, 22752], 'label': '31104.fx.1296.hm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '1296.hm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.hm1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247230
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.hn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cn1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.jg1', '432.jh1', '432.ji1', '648.bg1', '648.hl1', '648.hm1', '648.hp1', '648.hq1', '648.il1', '648.js1'], 'contains': ['2592.db1', '2592.dt2', '2592.ee1', '3888.bn1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [3943, 16092, 18576, 22752], 'label': '31104.fx.1296.hn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '1296.hn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.hn1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247231
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ho1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.ia1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.jj1', '432.jk1', '648.bj1', '648.gj1', '648.hh1', '648.hk1', '648.hm1', '648.jo1', '648.jt1'], 'contains': ['2592.db1', '2592.dz1', '2592.eb1', '3888.bo1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 14802, 18576, 10368], 'label': '31104.fx.1296.ho1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '1296.ho1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ho1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247232
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.hp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.il1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.jl1', '432.jn1', '648.bk1', '648.gk1', '648.hi1', '648.hj1', '648.hl1', '648.jo1', '648.jt1'], 'contains': ['2592.db1', '2592.eb1', '2592.eg1', '3888.bp1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [8305, 14802, 18576, 10368], 'label': '31104.fx.1296.hp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '1296.hp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.hp1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247233
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.hq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.ij1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.jm1', '432.jo1', '648.bi1', '648.gk1', '648.hm1', '648.ho1', '648.hs1', '648.jm1', '648.jr1'], 'contains': ['2592.db1', '2592.ed1', '2592.ef1', '3888.bq1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [29077, 14802, 18576, 10368], 'label': '31104.fx.1296.hq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '1296.hq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.hq1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247234
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.hr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.gn1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.jp1', '432.jr1', '648.bj1', '648.gl1', '648.ho1', '648.hq1', '648.hr1', '648.jp1', '648.jt1'], 'contains': ['2592.cy1', '2592.db1', '2592.dz1', '2592.fq1', '3888.br1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 12138, 18576, 10368], 'label': '31104.fx.1296.hr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '1296.hr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.hr1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247235
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.hs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.gr1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.jq1', '432.js1', '648.bk1', '648.gm1', '648.hn1', '648.hp1', '648.hs1', '648.jp1', '648.jt1'], 'contains': ['2592.cy1', '2592.db1', '2592.eg1', '3888.bs1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [8305, 12138, 18576, 10368], 'label': '31104.fx.1296.hs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '1296.hs1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.hs1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247236
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.g1', '18.h1', '27.a1'], 'contains': ['108.dn1', '108.ef1', '108.ep1', '162.o1', '162.p1', '864.gm1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [24198, 15624, 15984, 36, 16080, 15552, 2592, 12460], 'label': '31104.fx.54.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.o1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.o1', 'subgroup_fusion': None, 'weyl_group': '576.8654'}
-
id: 186247237
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ht1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.ht1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.jt1', '432.ju1', '648.x1', '648.gj1', '648.hj1', '648.ht1', '648.hz1', '648.iu1', '648.ju1'], 'contains': ['2592.dc1', '2592.dg1', '2592.eb1', '3888.bt1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [26485, 14730, 22752, 18576], 'label': '31104.fx.1296.ht1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '1296.ht1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ht1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 186247238
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.hu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cr1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.jv1', '432.jw1', '432.jx1', '648.m1', '648.gr1', '648.gs1', '648.hz1', '648.ia1', '648.jj1', '648.jw1'], 'contains': ['2592.dc1', '2592.do1', '2592.ec1', '3888.bu1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [19135, 18684, 18576, 22752], 'label': '31104.fx.1296.hu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '1296.hu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.hu1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247239
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.hv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cn1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.jy1', '432.jz1', '432.ka1', '648.bg1', '648.gv1', '648.gw1', '648.ht1', '648.hu1', '648.il1', '648.jw1'], 'contains': ['2592.dc1', '2592.dt2', '2592.ec1', '3888.bv1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [19135, 16092, 18576, 22752], 'label': '31104.fx.1296.hv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '1296.hv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.hv1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247240
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.hw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bt1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.kb1', '432.kc1', '648.bl1', '648.gj1', '648.gr1', '648.ho1', '648.hu1', '648.jv1', '648.kb1'], 'contains': ['2592.dc1', '2592.dz1', '2592.ef1', '3888.bw1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 2670, 18576, 10368], 'label': '31104.fx.1296.hw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '1296.hw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.hw1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247241
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.hx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.hx1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.kd1', '432.kf1', '648.y1', '648.gk1', '648.hk1', '648.hu1', '648.ia1', '648.iu1', '648.ju1'], 'contains': ['2592.dc1', '2592.eb1', '2592.ed1', '3888.bx1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [29077, 14730, 22752, 18576], 'label': '31104.fx.1296.hx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '1296.hx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.hx1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 186247242
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.hy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bx1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.ke1', '432.kg1', '648.bm1', '648.gk1', '648.gs1', '648.hn1', '648.ht1', '648.jv1', '648.kb1'], 'contains': ['2592.dc1', '2592.ef1', '2592.eg1', '3888.by1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [8305, 2670, 18576, 10368], 'label': '31104.fx.1296.hy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '1296.hy1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.hy1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247243
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.hz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.hl1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.jt1', '432.kj1', '648.bh1', '648.gd1', '648.gv1', '648.hv1', '648.hz1', '648.jl1', '648.jx1'], 'contains': ['2592.dd1', '2592.dg1', '2592.ec1', '3888.bt1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26485, 14730, 18576, 10368], 'label': '31104.fx.1296.hz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '1296.hz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.hz1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247244
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ia1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.ho1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.ju1', '432.kj1', '648.z1', '648.ge1', '648.gx1', '648.hw1', '648.ib1', '648.iy1', '648.jy1'], 'contains': ['2592.de1', '2592.di1', '2592.ej1', '3888.bt1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26485, 14730, 18576, 12096], 'label': '31104.fx.1296.ia1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '1296.ia1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ia1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247245
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ib1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cr1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.jx1', '432.kk1', '648.j1', '648.hh1', '648.hi1', '648.hz1', '648.ia1', '648.iv1', '648.ke1'], 'contains': ['2592.dd1', '2592.do1', '2592.eb1', '3888.bu1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [29503, 18684, 18576, 10368], 'label': '31104.fx.1296.ib1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '1296.ib1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ib1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247246
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ic1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.ct1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.jv1', '432.kk1', '648.k1', '648.gt1', '648.gu1', '648.ib1', '648.ic1', '648.iw1', '648.kf1'], 'contains': ['2592.de1', '2592.dq1', '2592.ej1', '3888.bu1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [26047, 108, 18576, 12096], 'label': '31104.fx.1296.ic1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '1296.ic1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ic1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247247
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.i1', '18.j1', '27.a1'], 'contains': ['108.dn1', '108.fk1', '108.fy1', '162.q1', '162.r1', '216.ea1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [20737, 15624, 15984, 36, 16080, 15552, 18144, 12460], 'label': '31104.fx.54.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.p1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.p1', 'subgroup_fusion': None, 'weyl_group': '576.8654'}
-
id: 186247248
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.id1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.jw1', '432.kk1', '648.l1', '648.ix1', '648.kg1'], 'contains': ['2592.df1', '2592.dr1', '2592.ek1', '3888.bu1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [6, 18180, 16056, 12096], 'label': '31104.fx.1296.id1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.k1', 'old_label': '1296.id1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.id1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247249
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ie1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cp1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.ka1', '432.kl1', '648.ba1', '648.hj1', '648.hk1', '648.hv1', '648.hy1', '648.ig1', '648.ke1'], 'contains': ['2592.dd1', '2592.dt1', '2592.eb1', '3888.bv1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [29503, 16092, 18576, 10368], 'label': '31104.fx.1296.ie1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '1296.ie1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ie1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247250
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.if1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cn1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.jy1', '432.kl1', '648.bb1', '648.gx1', '648.gy1', '648.hw1', '648.hx1', '648.ih1', '648.kf1'], 'contains': ['2592.de1', '2592.dv1', '2592.ej1', '3888.bv1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [26047, 2700, 18576, 12096], 'label': '31104.fx.1296.if1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '1296.if1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.if1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247251
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ig1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.jz1', '432.kl1', '648.bc1', '648.ii1', '648.kg1'], 'contains': ['2592.df1', '2592.dw1', '2592.ek1', '3888.bv1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [6, 468, 16056, 12096], 'label': '31104.fx.1296.ig1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.k1', 'old_label': '1296.ig1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ig1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247252
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ih1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bo1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.kb1', '432.km1', '648.bn1', '648.ge1', '648.gt1', '648.he1', '648.hx1', '648.jz1', '648.ki1'], 'contains': ['2592.de1', '2592.dy1', '2592.em1', '3888.bw1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 2598, 18576, 12096], 'label': '31104.fx.1296.ih1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '1296.ih1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ih1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247253
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ii1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bl1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.kc1', '432.km1', '648.bl1', '648.gd1', '648.hh1', '648.hq1', '648.hy1', '648.ka1', '648.kh1'], 'contains': ['2592.dd1', '2592.dz1', '2592.ee1', '3888.bw1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 2598, 18576, 10368], 'label': '31104.fx.1296.ii1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '1296.ii1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ii1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247254
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ij1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.hq1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.kf1', '432.kn1', '648.bi1', '648.gf1', '648.gw1', '648.hy1', '648.ia1', '648.jl1', '648.jx1'], 'contains': ['2592.dd1', '2592.ec1', '2592.ed1', '3888.bx1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [29077, 14730, 18576, 10368], 'label': '31104.fx.1296.ij1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '1296.ij1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ij1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247255
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ik1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bq1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.kg1', '432.ko1', '648.bm1', '648.gf1', '648.hi1', '648.hp1', '648.hv1', '648.ka1', '648.kh1'], 'contains': ['2592.dd1', '2592.ee1', '2592.eg1', '3888.by1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [8305, 2598, 18576, 10368], 'label': '31104.fx.1296.ik1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '1296.ik1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ik1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247256
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.il1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.hp1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.kd1', '432.kn1', '648.bd1', '648.gg1', '648.gy1', '648.hx1', '648.ic1', '648.iy1', '648.jy1'], 'contains': ['2592.de1', '2592.ej1', '2592.el1', '3888.bx1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [29077, 14730, 18576, 12096], 'label': '31104.fx.1296.il1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '1296.il1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.il1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247257
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.im1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bp1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.ke1', '432.ko1', '648.bo1', '648.gg1', '648.gu1', '648.hd1', '648.hw1', '648.jz1', '648.ki1'], 'contains': ['2592.de1', '2592.em1', '2592.eo1', '3888.by1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [8305, 2598, 18576, 12096], 'label': '31104.fx.1296.im1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '1296.im1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.im1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247258
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.g1', '18.k1', '18.l1', '27.c1'], 'contains': ['108.dq1', '108.dy1', '108.ek1', '162.o1', '162.s1', '216.jq1'], 'core': '216.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [24198, 18576, 2592, 36, 2664, 22752, 15552, 20812], 'label': '31104.fx.54.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '54.q1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.q1', 'subgroup_fusion': None, 'weyl_group': '1152.155790'}
-
id: 186247259
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.in1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bi1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.kh1', '432.kp1', '648.bl1', '648.gl1', '648.gw1', '648.hk1', '648.hz1', '648.kb1', '648.kh1'], 'contains': ['2592.dc1', '2592.dd1', '2592.dz1', '2592.fs1', '3888.bz1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 6, 18576, 10368], 'label': '31104.fx.1296.in1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '1296.in1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.in1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247260
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.io1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bk1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.ki1', '432.kq1', '648.bm1', '648.gm1', '648.gv1', '648.hj1', '648.ia1', '648.kb1', '648.kh1'], 'contains': ['2592.dc1', '2592.dd1', '2592.eg1', '3888.ca1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [8305, 6, 18576, 10368], 'label': '31104.fx.1296.io1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '1296.io1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.io1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247261
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ip1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.kp1', '648.bn1', '648.gh1', '648.gy1', '648.ib1', '648.ki1'], 'contains': ['2592.de1', '2592.dy1', '2592.fv1', '3888.bz1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [5713, 6, 18576, 12096], 'label': '31104.fx.1296.ip1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '1296.ip1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ip1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247262
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.iq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.kq1', '648.bo1', '648.gi1', '648.gx1', '648.ic1', '648.ki1'], 'contains': ['2592.de1', '2592.eo1', '3888.ca1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [8305, 6, 18576, 12096], 'label': '31104.fx.1296.iq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '1296.iq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.iq1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247263
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ir1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.q1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.kr1', '432.ku1', '648.n1', '648.gr1', '648.hh1', '648.hr1', '648.hz1', '648.kj1', '648.kj2'], 'contains': ['2592.dg1', '2592.do1', '2592.dz1', '2592.fw1', '3888.cb1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1, 15588, 2592, 10368], 'label': '31104.fx.1296.ir1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '1296.ir1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ir1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247264
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.is1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.kr1', '432.kv1', '648.o1', '648.kk1'], 'contains': ['2592.dh1', '2592.dp1', '2592.ea1', '2592.fx1', '2592.fx2', '3888.cb1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [20737, 15588, 2592, 12384], 'label': '31104.fx.1296.is1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.n1', 'old_label': '1296.is1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.is1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 186247265
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.it1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.ks1', '432.kw1', '648.br1', '648.gv1', '648.hl1', '648.hp1', '648.ht1', '648.in2', '648.kj1'], 'contains': ['2592.dg1', '2592.dt2', '2592.eg1', '3888.cc1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [15985, 16020, 2592, 10368], 'label': '31104.fx.1296.it1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '1296.it1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.it1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247266
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.it2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.p1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.ks1', '432.kw2', '648.br1', '648.gz1', '648.hj1', '648.hn1', '648.hv1', '648.in1', '648.kj2'], 'contains': ['2592.dg1', '2592.dt1', '2592.eg1', '3888.cc1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [15985, 468, 2592, 10368], 'label': '31104.fx.1296.it2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '1296.it2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.it2', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247267
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.iu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.ks1', '432.kx1', '648.bs1', '648.io1', '648.kk1'], 'contains': ['2592.dh1', '2592.du1', '2592.ei1', '3888.cc1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [8209, 3060, 2592, 12384], 'label': '31104.fx.1296.iu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.n1', 'old_label': '1296.iu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.iu1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247268
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.iv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.iv1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.kt1', '432.ky1', '648.x1', '648.gn1', '648.hh1', '648.hl1', '648.hv1', '648.iz1', '648.ju1'], 'contains': ['2592.dg1', '2592.eb1', '2592.ee1', '3888.cd1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [26485, 12210, 22752, 18576], 'label': '31104.fx.1296.iv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '1296.iv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.iv1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 186247269
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.h1', '18.l1', '27.b1'], 'contains': ['108.dp1', '108.ec1', '108.eh1', '162.o1', '162.u1', '216.js1'], 'core': '648.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [24198, 18576, 2592, 36, 2664, 10368, 15552, 22828], 'label': '31104.fx.54.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '54.r1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.r1', 'subgroup_fusion': None, 'weyl_group': '1152.155790'}
-
id: 186247270
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.iw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.iw1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.kt1', '432.kz1', '648.bh1', '648.gn1', '648.gr1', '648.gz1', '648.ht1', '648.jm1', '648.jx1'], 'contains': ['2592.dg1', '2592.ec1', '2592.ef1', '3888.cd1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26485, 12210, 18576, 10368], 'label': '31104.fx.1296.iw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '1296.iw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.iw1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247271
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ix1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ku1', '432.kv1', '648.p1', '648.gt1', '648.hf1', '648.ib1', '648.kl1'], 'contains': ['2592.di1', '2592.dq1', '2592.dy1', '2592.gb1', '3888.cb1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [20737, 15588, 2592, 1728], 'label': '31104.fx.1296.ix1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '1296.ix1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ix1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247272
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.iy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.kw1', '432.kw2', '432.kx1', '648.bu1', '648.gx1', '648.ha1', '648.hd1', '648.hw1', '648.ip1', '648.kl1'], 'contains': ['2592.di1', '2592.dv1', '2592.eo1', '3888.cc1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5617, 468, 2592, 1728], 'label': '31104.fx.1296.iy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '1296.iy1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.iy1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247273
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.iz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.jm1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.ky1', '432.kz1', '648.z1', '648.go1', '648.gt1', '648.ha1', '648.hw1', '648.ja1', '648.jy1'], 'contains': ['2592.di1', '2592.ej1', '2592.em1', '3888.cd1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26485, 12210, 18576, 12096], 'label': '31104.fx.1296.iz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '1296.iz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.iz1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247274
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ja1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.u1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.la1', '432.lb1', '648.q1', '648.gs1', '648.hi1', '648.hs1', '648.ia1', '648.kj1', '648.kj2'], 'contains': ['2592.do1', '2592.ed1', '2592.eg1', '3888.ce1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [15985, 15588, 2592, 10368], 'label': '31104.fx.1296.ja1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '1296.ja1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ja1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247275
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.jb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.lb1', '432.lc1', '648.s1', '648.kk1'], 'contains': ['2592.dp1', '2592.eh1', '2592.ei1', '3888.ce1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [8209, 15588, 2592, 12384], 'label': '31104.fx.1296.jb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.n1', 'old_label': '1296.jb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.jb1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 186247276
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.jc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.w1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.la1', '432.lc1', '648.v1', '648.gu1', '648.hg1', '648.ic1', '648.kl1'], 'contains': ['2592.dq1', '2592.el1', '2592.eo1', '3888.ce1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [5617, 15588, 2592, 1728], 'label': '31104.fx.1296.jc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '1296.jc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.jc1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247277
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.jd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.ld1', '432.ld2', '432.le1', '648.cg1', '648.gy1', '648.hb1', '648.he1', '648.hx1', '648.ip1', '648.kl1'], 'contains': ['2592.dv1', '2592.dy1', '2592.el1', '3888.cf1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [20737, 468, 2592, 1728], 'label': '31104.fx.1296.jd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '1296.jd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.jd1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247278
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.je1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.ld1', '432.lf1', '648.ch1', '648.gw1', '648.hm1', '648.hq1', '648.hu1', '648.in2', '648.kj1'], 'contains': ['2592.dt2', '2592.dz1', '2592.ed1', '3888.cf1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1, 16020, 2592, 10368], 'label': '31104.fx.1296.je1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '1296.je1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.je1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247279
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.je2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.p1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.ld2', '432.lf1', '648.ch1', '648.hc1', '648.hk1', '648.ho1', '648.hy1', '648.in1', '648.kj2'], 'contains': ['2592.dt1', '2592.dz1', '2592.ed1', '3888.cf1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1, 468, 2592, 10368], 'label': '31104.fx.1296.je2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '1296.je2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.je2', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247280
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.g1', '18.n1', '27.b1'], 'contains': ['108.dp1', '108.eb1', '108.ev1', '162.p1', '162.s1', '216.jr1'], 'core': '648.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [24198, 16056, 432, 36, 22752, 15552, 18144, 16080], 'label': '31104.fx.54.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '54.s1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.s1', 'subgroup_fusion': None, 'weyl_group': '3456.di'}
-
id: 186247281
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.jf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.le1', '432.lf1', '648.ci1', '648.io1', '648.kk1'], 'contains': ['2592.du1', '2592.ea1', '2592.eh1', '3888.cf1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [20737, 3060, 2592, 12384], 'label': '31104.fx.1296.jf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.n1', 'old_label': '1296.jf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.jf1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247282
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.jg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cu1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.lg1', '432.lj1', '648.ba1', '648.hl1', '648.hm1', '648.ht1', '648.hu1', '648.iq1', '648.iv1'], 'contains': ['2592.dt2', '2592.eb1', '2592.ef1', '3888.cg1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [14311, 2628, 18576, 10368], 'label': '31104.fx.1296.jg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '1296.jg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.jg1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247283
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.jh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cv1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.lh1', '432.li1', '432.lj1', '648.bg1', '648.gz1', '648.hc1', '648.hv1', '648.hy1', '648.ir1', '648.jj1'], 'contains': ['2592.dt1', '2592.ec1', '2592.ee1', '3888.cg1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [3943, 2628, 18576, 22752], 'label': '31104.fx.1296.jh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '1296.jh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.jh1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247284
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ji1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cu1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.lg1', '432.lh1', '648.bb1', '648.ha1', '648.hb1', '648.hw1', '648.hx1', '648.is1', '648.iw1'], 'contains': ['2592.dv1', '2592.ej1', '2592.em1', '3888.cg1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [28567, 2628, 18576, 12096], 'label': '31104.fx.1296.ji1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '1296.ji1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ji1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247285
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.jj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cu1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.lg1', '432.li1', '648.bc1', '648.it1', '648.ix1'], 'contains': ['2592.dw2', '2592.ek1', '2592.en1', '3888.cg1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [18150, 18612, 16056, 12096], 'label': '31104.fx.1296.jj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.k1', 'old_label': '1296.jj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.jj1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 186247286
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.jk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.jk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.lk1', '648.be1', '648.go1', '648.hx1', '648.ib1', '648.jb1'], 'contains': ['2592.dy1', '2592.ej1', '3888.ch1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [5713, 12210, 12096, 18576], 'label': '31104.fx.1296.jk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '1296.jk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.jk1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 186247287
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.jl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.ch1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ll1', '648.bn1', '648.go1', '648.hb1', '648.hf1', '648.jz1'], 'contains': ['2592.dy1', '2592.em1', '3888.ci1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [5713, 78, 18576, 12096], 'label': '31104.fx.1296.jl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '1296.jl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.jl1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247288
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.jm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.iz1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.lk1', '432.lm1', '648.bj1', '648.gn1', '648.hu1', '648.hy1', '648.hz1', '648.jc1', '648.jo1'], 'contains': ['2592.dz1', '2592.eb1', '2592.ec1', '3888.ch1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 12210, 18576, 10368], 'label': '31104.fx.1296.jm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '1296.jm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.jm1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247289
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.jn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.ll1', '432.ln1', '648.bl1', '648.gn1', '648.hc1', '648.hm1', '648.hr1', '648.jv1', '648.ka1'], 'contains': ['2592.dz1', '2592.ee1', '2592.ef1', '3888.ci1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 78, 18576, 10368], 'label': '31104.fx.1296.jn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '1296.jn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.jn1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247290
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.jo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.jo1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.lo1', '432.ls1', '648.y1', '648.gp1', '648.hi1', '648.hm1', '648.hy1', '648.iz1', '648.ju1'], 'contains': ['2592.eb1', '2592.ed1', '2592.ee1', '3888.cj1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [29077, 12210, 22752, 18576], 'label': '31104.fx.1296.jo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '1296.jo1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.jo1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247291
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.h1', '18.m1', '18.n1', '27.c1'], 'contains': ['108.a1', '108.dq1', '108.ej1', '162.p1', '162.u1', '216.jt1'], 'core': '108.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [19135, 16056, 18576, 36, 22752, 15552, 2592, 15484], 'label': '31104.fx.54.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '54.t1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.t1', 'subgroup_fusion': None, 'weyl_group': '3456.di'}
-
id: 186247292
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.jp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.jp1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.lp1', '432.ls1', '648.bi1', '648.gp1', '648.gs1', '648.hc1', '648.hu1', '648.jm1', '648.jx1'], 'contains': ['2592.ec1', '2592.ed1', '2592.ef1', '3888.cj1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [29077, 12210, 18576, 10368], 'label': '31104.fx.1296.jp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '1296.jp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.jp1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247293
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.jq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.js1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.lq1', '432.lt1', '648.bk1', '648.gp1', '648.ht1', '648.hv1', '648.ia1', '648.jc1', '648.jo1'], 'contains': ['2592.eb1', '2592.ec1', '2592.eg1', '3888.ck1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [8305, 12210, 18576, 10368], 'label': '31104.fx.1296.jq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '1296.jq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.jq1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247294
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.jr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cj1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.lr1', '432.lu1', '648.bm1', '648.gp1', '648.gz1', '648.hl1', '648.hs1', '648.jv1', '648.ka1'], 'contains': ['2592.ee1', '2592.ef1', '2592.eg1', '3888.cl1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [8305, 78, 18576, 10368], 'label': '31104.fx.1296.jr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '1296.jr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.jr1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247295
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.js1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.jq1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.lo1', '432.lp1', '648.bd1', '648.gq1', '648.gu1', '648.hb1', '648.hx1', '648.ja1', '648.jy1'], 'contains': ['2592.ej1', '2592.el1', '2592.em1', '3888.cj1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [29077, 78, 18576, 12096], 'label': '31104.fx.1296.js1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '1296.js1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.js1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247296
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.jt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.jt1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.lq1', '648.bf1', '648.gq1', '648.hw1', '648.ic1', '648.jb1'], 'contains': ['2592.ej1', '2592.eo1', '3888.ck1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [8305, 12210, 12096, 18576], 'label': '31104.fx.1296.jt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '1296.jt1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.jt1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 186247297
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ju1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.ck1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.lr1', '648.bo1', '648.gq1', '648.ha1', '648.hg1', '648.jz1'], 'contains': ['2592.em1', '2592.eo1', '3888.cl1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [8305, 78, 18576, 12096], 'label': '31104.fx.1296.ju1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '1296.ju1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ju1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247298
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.jv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.df1', '432.lv1', '432.lw1', '432.lx1', '648.id1', '648.ie1', '648.if1'], 'contains': ['2592.et1', '3888.cm1', '5184.p1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [36, 12460, 2664, 18576], 'label': '31104.fx.1296.jv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.el1', 'old_label': '1296.jv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.jv1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 186247299
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.jw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.bc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.lv1', '432.ly1', '432.mb1', '648.cn1', '648.ig1', '648.im1', '648.in1', '648.ir1'], 'contains': ['2592.ct1', '2592.dt1', '2592.ep1', '3888.cm1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [36, 16056, 432, 22752], 'label': '31104.fx.1296.jw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '1296.jw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.jw1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 186247300
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.jw2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.lw1', '432.lz1', '432.ma1', '432.mb1', '648.cn1', '648.ij1', '648.il1', '648.in2', '648.iq1'], 'contains': ['2592.ct1', '2592.dt2', '2592.ep2', '3888.cm1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [36, 16056, 432, 10368], 'label': '31104.fx.1296.jw2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '1296.jw2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.jw2', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 186247301
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.jx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.lx1', '432.mb1', '432.mc1', '648.co1', '648.io1'], 'contains': ['2592.cu1', '2592.du1', '2592.eq1', '3888.cm1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [36, 16056, 432, 12384], 'label': '31104.fx.1296.jx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.z1', 'old_label': '1296.jx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.jx1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 186247302
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.i1', '18.o1'], 'contains': ['108.cl1', '108.co1', '108.da1', '108.dg1', '108.do1', '108.ez1', '108.fn1', '162.q1', '162.v1', '216.eb1'], 'core': '648.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1, 12940, 10368, 36, 15552, 18144, 18216, 18576], 'label': '31104.fx.54.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.u1', 'old_label': '54.u1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.u1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
-
id: 186247303
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.jy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.ly1', '432.lz1', '432.mc1', '648.cp1', '648.cq1', '648.ih1', '648.ik1', '648.ip1', '648.is1', '648.it1'], 'contains': ['2592.cv1', '2592.cw1', '2592.dv1', '2592.dw2', '2592.er1', '3888.cm1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [36, 2592, 18576, 12096], 'label': '31104.fx.1296.jy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '1296.jy1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.jy1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 186247304
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.jz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.ly1', '432.ma1', '432.mc1', '648.cq1', '648.cr1', '648.ii1'], 'contains': ['2592.cw1', '2592.cx1', '2592.dw1', '2592.dx1', '2592.es1', '3888.cm1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [36, 504, 15984, 12096], 'label': '31104.fx.1296.jz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.t1', 'old_label': '1296.jz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.jz1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 186247305
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ka1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.mr1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.md1', '432.mj1', '432.mk1', '648.cs1', '648.ig1', '648.iu1', '648.iv1', '648.iz1', '648.jc1', '648.jt1'], 'contains': ['2592.cy1', '2592.eb1', '2592.ep1', '3888.cn1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [17371, 16056, 10368, 18576], 'label': '31104.fx.1296.ka1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '1296.ka1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ka1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 186247306
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.kb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.mh1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.md1', '432.mh1', '648.ct1', '648.ih1', '648.iw1', '648.iy1', '648.ja1', '648.jb1', '648.jn1'], 'contains': ['2592.cz1', '2592.ej1', '2592.er1', '3888.cn1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [12138, 2592, 12096, 18576], 'label': '31104.fx.1296.kb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '1296.kb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.kb1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 186247307
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.kc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.gc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.md1', '432.mi1', '648.cu1', '648.ii1', '648.ix1'], 'contains': ['2592.da1', '2592.ek1', '2592.es1', '3888.cn1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [17371, 504, 12096, 15984], 'label': '31104.fx.1296.kc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.j1', 'old_label': '1296.kc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.kc1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 186247308
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.kd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.me1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.me1', '432.mf1', '432.mg1', '432.mo1', '648.cs1', '648.ij1', '648.jd1', '648.jh1', '648.jp1'], 'contains': ['2592.cy1', '2592.ep2', '3888.co1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [17371, 18576, 2592, 10368], 'label': '31104.fx.1296.kd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '1296.kd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.kd1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186247309
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ke1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.me1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.me1', '432.ml1', '648.ct1', '648.cu1', '648.ik1', '648.je1', '648.ji1', '648.ji2', '648.jn1'], 'contains': ['2592.cz1', '2592.da1', '2592.er1', '3888.co1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [12138, 16056, 18576, 12096], 'label': '31104.fx.1296.ke1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '1296.ke1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ke1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
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id: 186247310
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.kf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.fa1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.dl1', '432.mf1', '432.mm1', '648.id1', '648.jf1', '648.jq1'], 'contains': ['2592.et1', '3888.co1', '5184.v1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [12138, 20812, 2664, 18576], 'label': '31104.fx.1296.kf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ge1', 'old_label': '1296.kf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.kf1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186247311
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.kg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.dm1', '432.mg1', '432.mn1', '648.jg1'], 'contains': ['2592.ev1', '3888.co1', '5184.w1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [17371, 29904, 15984, 2592], 'label': '31104.fx.1296.kg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ks1', 'old_label': '1296.kg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.kg1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186247312
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.kh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.mh1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.mh1', '432.mi1', '432.mk1', '432.mp1', '648.cv1', '648.il1', '648.jj1', '648.jl1', '648.jm1', '648.jo1', '648.jp1'], 'contains': ['2592.db1', '2592.ec1', '2592.ep2', '3888.cn1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [12138, 432, 16056, 10368], 'label': '31104.fx.1296.kh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '1296.kh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.kh1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247313
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.i1', '18.p1', '27.b1'], 'contains': ['108.dp1', '108.fa1', '108.fo1', '162.r1', '162.v1', '216.ed1', '216.ju1'], 'core': '648.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [20737, 16056, 432, 36, 22752, 15552, 2592, 16080], 'label': '31104.fx.54.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '54.v1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.v1', 'subgroup_fusion': None, 'weyl_group': '1152.155790'}
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id: 186247314
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ki1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.fc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.do1', '432.mj1', '432.mp1', '648.ie1', '648.jk1', '648.jq1'], 'contains': ['2592.et1', '3888.cn1', '5184.y1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [17371, 7780, 16056, 18576], 'label': '31104.fx.1296.ki1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.gd1', 'old_label': '1296.ki1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ki1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186247315
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.kj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ne1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.ml1', '432.mm1', '432.mn1', '432.mo1', '648.cv1', '648.im1', '648.jr1', '648.js1', '648.jt1'], 'contains': ['2592.db1', '2592.ep1', '3888.co1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [12138, 16056, 18576, 10368], 'label': '31104.fx.1296.kj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '1296.kj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.kj1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186247316
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.kk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.ka1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.mr1', '432.ms1', '432.mt1', '432.mu1', '432.mv1', '432.mv2', '432.mw1', '648.cw1', '648.il1', '648.jd1', '648.jj1', '648.ju1', '648.jv1', '648.kh1'], 'contains': ['2592.dc1', '2592.ee1', '2592.ep2', '3888.cp1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [6, 432, 10368, 16056], 'label': '31104.fx.1296.kk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '1296.kk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.kk1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247317
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.kl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.kl1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.mq1', '432.mx1', '432.na1', '648.cw1', '648.im1', '648.iu1', '648.jw1', '648.kb1'], 'contains': ['2592.dc1', '2592.ep1', '3888.cq1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [26047, 18576, 2592, 22752], 'label': '31104.fx.1296.kl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '1296.kl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.kl1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186247318
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.km1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.fc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.dq1', '432.mq1', '432.my1', '648.id1', '648.jk1', '648.kc1'], 'contains': ['2592.et1', '3888.cq1', '5184.ba1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [6, 20812, 2664, 18576], 'label': '31104.fx.1296.km1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.gd1', 'old_label': '1296.km1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.km1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186247319
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.kn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.z1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.dr1', '432.mq1', '432.mz1', '648.kd1'], 'contains': ['2592.eu1', '3888.cq1', '5184.bb1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [26047, 28464, 15984, 2592], 'label': '31104.fx.1296.kn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.mc1', 'old_label': '1296.kn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.kn1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186247320
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ko1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.ko1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.mw1', '432.nb1', '432.nc1', '432.nd1', '648.cx1', '648.ig1', '648.iv1', '648.jr1', '648.jx1', '648.ka1', '648.kb1'], 'contains': ['2592.dd1', '2592.ef1', '2592.ep1', '3888.cp1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26047, 16056, 18576, 10368], 'label': '31104.fx.1296.ko1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '1296.ko1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ko1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247321
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.kp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.ka1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.mr1', '432.nb1', '648.cy1', '648.ih1', '648.iw1', '648.je1', '648.jy1', '648.jz1', '648.ki1'], 'contains': ['2592.de1', '2592.em1', '2592.er1', '3888.cp1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [6, 2592, 18576, 12096], 'label': '31104.fx.1296.kp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '1296.kp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.kp1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247322
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.kq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ep1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.ms1', '432.nb1', '648.cz1', '648.ii1', '648.ix1'], 'contains': ['2592.df1', '2592.en1', '2592.es1', '3888.cp1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [6, 432, 16056, 12096], 'label': '31104.fx.1296.kq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.k1', 'old_label': '1296.kq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.kq1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247323
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.kr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.fa1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.du1', '432.mt1', '432.nc1', '648.ie1', '648.jf1', '648.kc1'], 'contains': ['2592.et1', '3888.cp1', '5184.be1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [26047, 7780, 16056, 18576], 'label': '31104.fx.1296.kr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ge1', 'old_label': '1296.kr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.kr1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186247324
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.i1', '18.p1', '18.q1', '27.c1'], 'contains': ['108.dq1', '108.fb1', '108.fp1', '162.r1', '162.v1', '216.ee1', '216.jv1'], 'core': '216.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1, 16056, 432, 36, 10368, 15552, 2592, 16080], 'label': '31104.fx.54.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '54.w1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.w1', 'subgroup_fusion': None, 'weyl_group': '1152.155790'}
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id: 186247325
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ks1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.bc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.dv1', '432.mu1', '432.nc1', '648.kd1'], 'contains': ['2592.eu1', '3888.cp1', '5184.bf1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [26047, 18148, 16056, 18576], 'label': '31104.fx.1296.ks1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ma1', 'old_label': '1296.ks1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ks1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186247326
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.kt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.dw1', '432.mv1', '432.nd1', '648.jg1'], 'contains': ['2592.ev1', '3888.cp1', '5184.bg1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [6, 19536, 18576, 2592], 'label': '31104.fx.1296.kt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ks1', 'old_label': '1296.kt1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.kt1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186247327
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.kt2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.dw1', '432.mv2', '432.nd1'], 'contains': ['2592.ev2', '3888.cp1', '5184.bg1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [26047, 4540, 16056, 18576], 'label': '31104.fx.1296.kt2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.mv2', 'old_label': '1296.kt2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.kt2', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 186247328
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ku1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.kj1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.my1', '432.mz1', '432.na1', '432.ne1', '648.cx1', '648.ij1', '648.jl1', '648.ke1', '648.kh1'], 'contains': ['2592.dd1', '2592.ep2', '3888.cq1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [6, 16056, 18576, 22752], 'label': '31104.fx.1296.ku1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '1296.ku1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ku1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186247329
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.kv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.kj1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.mx1', '432.ne1', '648.cy1', '648.cz1', '648.ik1', '648.iy1', '648.kf1', '648.kg1', '648.ki1'], 'contains': ['2592.de1', '2592.df1', '2592.er1', '3888.cq1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [6, 16056, 18576, 12096], 'label': '31104.fx.1296.kv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '1296.kv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.kv1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
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id: 186247330
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.kw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.dg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.nf1', '432.ng1', '432.ni1', '432.nk2', '648.da1', '648.in1', '648.iu1', '648.iz1', '648.jr1', '648.jx1', '648.kj1'], 'contains': ['2592.dg1', '2592.ed1', '2592.ep1', '3888.cr1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [10405, 18576, 22752, 2592], 'label': '31104.fx.1296.kw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '1296.kw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.kw1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247331
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.kw2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.dd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.nf1', '432.nh1', '432.nj1', '432.nk1', '648.da1', '648.in2', '648.jd1', '648.jl1', '648.jm1', '648.ju1', '648.kj2'], 'contains': ['2592.dg1', '2592.ed1', '2592.ep2', '3888.cr1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [10405, 18576, 10368, 2592], 'label': '31104.fx.1296.kw2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '1296.kw2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.kw2', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247332
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.kx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.nf1', '432.nl1', '432.nm1', '432.nn1', '648.db1', '648.io1', '648.kk1'], 'contains': ['2592.dh1', '2592.eh1', '2592.eq1', '3888.cr1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [10405, 3024, 12384, 2592], 'label': '31104.fx.1296.kx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.n1', 'old_label': '1296.kx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.kx1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247333
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ky1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.dd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.ng1', '432.nh1', '432.nl1', '648.dc1', '648.ip1', '648.iy1', '648.ja1', '648.je1', '648.jy1', '648.kl1'], 'contains': ['2592.di1', '2592.el1', '2592.er1', '3888.cr1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [10405, 3024, 2592, 1728], 'label': '31104.fx.1296.ky1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '1296.ky1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ky1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247334
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.kz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ha1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.eb1', '432.ni1', '432.nj1', '432.nm1', '648.if1', '648.jf1', '648.jk1'], 'contains': ['2592.et1', '3888.cr1', '5184.bl1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [10405, 12460, 432, 2592], 'label': '31104.fx.1296.kz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.dj1', 'old_label': '1296.kz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.kz1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186247335
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '8.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': ['3888.cw1', '3888.cx1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '4.b1', '4.c1', '4.d1', '4.e1'], 'contains': ['24.a1', '24.b1', '24.n1', '24.o1', '24.p1', '32.a1'], 'core': '8.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [76, 15552, 10368, 16056, 5712, 22752, 18144, 18576, 12096], 'label': '31104.fx.8.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': ['4.a1', '4.b1', '4.c1', '4.d1', '4.e1'], 'normal_contains': ['24.a1', '24.b1'], 'normalizer': '1.a1', 'old_label': '8.a1', 'projective_image': '31104.fx', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.a1', 'subgroup_fusion': None, 'weyl_group': '3456.di'}
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id: 186247336
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.j1', '18.o1'], 'contains': ['108.cm1', '108.cp1', '108.db1', '108.dh1', '108.dr1', '108.ff1', '108.fs1', '162.q1', '162.w1', '216.ef1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [20737, 10924, 2016, 36, 15552, 18144, 18216, 18576], 'label': '31104.fx.54.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '54.x1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.x1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
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id: 186247337
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.la1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.bj1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.ed1', '432.nk1', '432.nk2', '432.nn1', '648.jg1'], 'contains': ['2592.ev1', '3888.cr1', '5184.bn1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [10405, 9168, 18576, 2592], 'label': '31104.fx.1296.la1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.es1', 'old_label': '1296.la1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.la1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186247338
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.lb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.no1', '432.no2', '432.nr1', '648.cn1', '648.dd1', '648.iv1', '648.js1', '648.jw1', '648.kj1', '648.kn1'], 'contains': ['2592.dj1', '2592.do1', '2592.dt2', '2592.ep1', '3888.cs1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [18180, 16056, 18576, 10368], 'label': '31104.fx.1296.lb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '1296.lb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.lb1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247339
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.lb2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.np1', '432.nq1', '432.nr1', '648.cn1', '648.dd1', '648.jh1', '648.jj1', '648.ke1', '648.kj2', '648.km1'], 'contains': ['2592.dj1', '2592.do1', '2592.dt1', '2592.ep2', '3888.cs1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [18180, 16056, 18576, 22752], 'label': '31104.fx.1296.lb2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '1296.lb2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.lb2', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247340
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.lc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.nr1', '432.ns1', '432.ns2', '648.co1', '648.de1', '648.kk1'], 'contains': ['2592.dk1', '2592.dk2', '2592.dp1', '2592.du1', '2592.eq1', '3888.cs1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [18180, 16056, 432, 12384], 'label': '31104.fx.1296.lc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.w1', 'old_label': '1296.lc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.lc1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247341
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ld1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.no1', '432.np1', '432.ns2', '648.cq1', '648.df1', '648.dg1', '648.ji1', '648.kg1', '648.ko1', '648.kp1'], 'contains': ['2592.dl1', '2592.dm2', '2592.dr1', '2592.dw1', '2592.er1', '3888.cs1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [15588, 2592, 18576, 12096], 'label': '31104.fx.1296.ld1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.t1', 'old_label': '1296.ld1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ld1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247342
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ld2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.no2', '432.np1', '432.ns1', '648.cp1', '648.dg1', '648.iw1', '648.ji2', '648.kf1', '648.kl1', '648.kp2'], 'contains': ['2592.dm1', '2592.dq1', '2592.dv1', '2592.er1', '3888.cs1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [108, 2592, 18576, 12096], 'label': '31104.fx.1296.ld2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '1296.ld2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ld2', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247343
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.le1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.no1', '432.nq1', '432.ns1', '432.ns2', '648.cr1', '648.dg1', '648.dh1'], 'contains': ['2592.dm1', '2592.dm2', '2592.dn1', '2592.dn3', '2592.ds1', '2592.dx1', '2592.es1', '3888.cs1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [16020, 432, 16056, 12096], 'label': '31104.fx.1296.le1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.di1', 'old_label': '1296.le1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.le1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247344
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.le2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.no2', '432.nq1', '432.ns2', '648.cq1', '648.dh1', '648.ix1'], 'contains': ['2592.dn1', '2592.dn2', '2592.dr1', '2592.dw2', '2592.es1', '3888.cs1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [18612, 504, 15984, 12096], 'label': '31104.fx.1296.le2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.t1', 'old_label': '1296.le2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.le2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 186247345
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.lf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.ct1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.nt1', '432.nu1', '432.nv1', '648.di1', '648.ip1', '648.jb1', '648.jn1', '648.jz1', '648.ki1', '648.kl1'], 'contains': ['2592.dy1', '2592.eo1', '2592.er1', '3888.ct1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1, 18576, 1728, 2592], 'label': '31104.fx.1296.lf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '1296.lf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.lf1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 186247346
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.lg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.cy1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.nt1', '432.nw1', '432.nz1', '648.dj1', '648.in1', '648.jc1', '648.jt1', '648.ka1', '648.kb1', '648.kj1'], 'contains': ['2592.dz1', '2592.eg1', '2592.ep1', '3888.ct1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1, 3024, 2592, 10368], 'label': '31104.fx.1296.lg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '1296.lg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.lg1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186247347
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.j1', '18.o1', '18.r1'], 'contains': ['108.cn1', '108.cq1', '108.dc1', '108.di1', '108.ds1', '108.fg1', '108.ft1', '162.q1', '162.w1', '216.eg1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [20737, 556, 12384, 36, 15552, 18144, 18216, 18576], 'label': '31104.fx.54.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.y1', 'old_label': '54.y1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.y1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
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id: 186247348
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.lg2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.ct1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.nu1', '432.nx1', '432.ny1', '432.nz1', '648.dj1', '648.in2', '648.jo1', '648.jp1', '648.jv1', '648.kh1', '648.kj2'], 'contains': ['2592.dz1', '2592.eg1', '2592.ep2', '3888.ct1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1, 3024, 2592, 22752], 'label': '31104.fx.1296.lg2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '1296.lg2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.lg2', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247349
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.lh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.nv1', '432.nz1', '432.oa1', '648.dk1', '648.io1', '648.kk1'], 'contains': ['2592.ea1', '2592.ei1', '2592.eq1', '3888.ct1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1, 3024, 2592, 12384], 'label': '31104.fx.1296.lh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.p1', 'old_label': '1296.lh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.lh1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247350
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.li1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.ei1', '432.nw1', '432.nx1', '432.oa1', '648.if1', '648.jq1', '648.kc1'], 'contains': ['2592.et1', '3888.ct1', '5184.bz1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [1, 20812, 432, 2592], 'label': '31104.fx.1296.li1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.el1', 'old_label': '1296.li1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.li1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186247351
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.lj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.ek1', '432.nw1', '432.ny1', '432.oa1', '648.kd1'], 'contains': ['2592.eu1', '3888.ct1', '5184.cb1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [1, 76, 432, 2592], 'label': '31104.fx.1296.lj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.kd1', 'old_label': '1296.lj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.lj1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186247352
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.lk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ob1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.ob1', '432.og1', '648.cs1', '648.dl1', '648.iq1', '648.jo1', '648.ju1', '648.ke1', '648.km1'], 'contains': ['2592.eb1', '2592.ep2', '3888.cu1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [2179, 2592, 10368, 18576], 'label': '31104.fx.1296.lk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '1296.lk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.lk1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
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id: 186247353
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ll1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.of1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.oc1', '432.od1', '432.og1', '648.cv1', '648.dm1', '648.ir1', '648.jc1', '648.jw1', '648.jx1', '648.kn1'], 'contains': ['2592.ec1', '2592.ep1', '3888.cu1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [30282, 18576, 16056, 10368], 'label': '31104.fx.1296.ll1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '1296.ll1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ll1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
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id: 186247354
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.lm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.lm1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.oe1', '432.oe2', '432.oh1', '648.cw1', '648.do1', '648.ir1', '648.iz1', '648.js1', '648.ka1', '648.kn1'], 'contains': ['2592.ee1', '2592.ep1', '3888.cv1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [18150, 18576, 10368, 16056], 'label': '31104.fx.1296.lm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '1296.lm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.lm1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
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id: 186247355
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ln1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.ll1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.of1', '432.oh1', '648.cx1', '648.dp1', '648.iq1', '648.jh1', '648.jm1', '648.jv1', '648.km1'], 'contains': ['2592.ef1', '2592.ep2', '3888.cv1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [10855, 2592, 18576, 10368], 'label': '31104.fx.1296.ln1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '1296.ln1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ln1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
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id: 186247356
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.lo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ob1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.ob1', '432.oc1', '648.ct1', '648.du1', '648.is1', '648.jb1', '648.jy1', '648.kf1', '648.ko1'], 'contains': ['2592.ej1', '2592.er1', '3888.cu1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [14730, 16056, 12096, 18576], 'label': '31104.fx.1296.lo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '1296.lo1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.lo1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
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id: 186247357
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.lp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ob1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.ob1', '432.od1', '648.cu1', '648.dt1', '648.du1', '648.it1', '648.kg1', '648.kp1', '648.kp2'], 'contains': ['2592.ek1', '2592.er1', '3888.cu1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [30282, 18576, 12096, 16056], 'label': '31104.fx.1296.lp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.ba1', 'old_label': '1296.lp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.lp1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 186247358
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.j1', '18.p1'], 'contains': ['108.dt1', '108.fh1', '108.fu1', '162.r1', '162.w1', '216.ej1', '216.ek1', '216.jw1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [20737, 16056, 432, 36, 12384, 15552, 2592, 16080], 'label': '31104.fx.54.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.z1', 'old_label': '54.z1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.z1', 'subgroup_fusion': None, 'weyl_group': '576.8660'}
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id: 186247359
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.lq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.ll1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.oe1', '432.of1', '648.cz1', '648.dw1', '648.dx1', '648.it1', '648.ji1', '648.ko1', '648.kp2'], 'contains': ['2592.en1', '2592.er1', '3888.cv1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [10495, 18576, 2592, 12096], 'label': '31104.fx.1296.lq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bb1', 'old_label': '1296.lq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.lq1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186247360
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.lq2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.ll1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.oe2', '432.of1', '648.cy1', '648.dx1', '648.is1', '648.ja1', '648.ji2', '648.jz1', '648.kp1'], 'contains': ['2592.em1', '2592.er1', '3888.cv1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [25975, 2592, 18576, 12096], 'label': '31104.fx.1296.lq2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '1296.lq2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.lq2', 'subgroup_fusion': None, 'weyl_group': '48.38'}
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id: 186247361
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.lr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.el1', '432.oi1', '432.oj1', '432.ok1'], 'contains': ['2592.ew1', '2592.ex1', '2592.ez1', '2592.fi1', '2592.fn1', '2592.fr1', '2592.ft1', '3888.cw1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 2592, 'diagramx': None, 'generators': [20737, 24198, 36, 16080], 'label': '31104.fx.1296.lr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1296.lr1', 'old_label': '1296.lr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.lr1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247362
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.ls1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ol1', '648.gh1'], 'contains': ['2592.fb1', '2592.ff1', '2592.fh1', '2592.fm1', '2592.fv1', '3888.cw1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [5713, 6, 36, 12096], 'label': '31104.fx.1296.ls1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.gh1', 'old_label': '1296.ls1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ls1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 186247363
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.lt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bi1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.oj1', '432.ok1', '432.ol1', '432.om1', '648.gl1'], 'contains': ['2592.fa1', '2592.fc1', '2592.fd1', '2592.fg1', '2592.fp1', '2592.fq1', '2592.fs1', '3888.cw1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [5713, 24198, 36, 10368], 'label': '31104.fx.1296.lt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.gl1', 'old_label': '1296.lt1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.lt1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 186247364
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.lu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.on1', '648.gh1'], 'contains': ['2592.fh1', '2592.fl1', '2592.fm1', '2592.fv1', '2592.gc1', '3888.cx1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [5713, 6, 18612, 12096], 'label': '31104.fx.1296.lu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.gh1', 'old_label': '1296.lu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.lu1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 186247365
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1296.lv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bi1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.on1', '432.oo1', '648.gl1'], 'contains': ['2592.fg1', '2592.fk1', '2592.fo1', '2592.fp1', '2592.fq1', '2592.fs1', '2592.fy1', '3888.cx1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [5713, 24198, 18612, 22752], 'label': '31104.fx.1296.lv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.gl1', 'old_label': '1296.lv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.lv1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 186247366
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.b1', '864.a1', '864.b1', '864.k1', '864.q1', '864.bc1', '864.bc2', '864.bh1', '864.bm1', '864.bm2', '864.br1', '864.bz1', '864.ca1', '864.cr1', '864.cs1', '864.cw1'], 'contains': ['3456.b1', '5184.a1', '5184.d1', '5184.e1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [18144, 12096, 10368], 'label': '31104.fx.1728.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '1728.a1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 186247367
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bj1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.hl1', '576.c1', '864.h1', '864.r1', '864.z1', '864.bu1', '864.cb1', '864.cc1', '864.cx1'], 'contains': ['3456.c1', '5184.a1', '5184.f1', '5184.g1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [3096, 10924, 22752], 'label': '31104.fx.1728.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bj1', 'old_label': '1728.b1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247368
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bm1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.hm1', '576.d1', '864.s1', '864.cd1', '864.dc1'], 'contains': ['3456.g1', '5184.a1', '5184.h1', '5184.i1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [18144, 22132, 11764], 'label': '31104.fx.1728.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.bv1', 'old_label': '1728.c1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247369
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.k1', '18.s1', '27.d1'], 'contains': ['108.j1', '108.q1', '108.y1', '108.bu1', '108.du1', '108.dx1', '108.eu1', '162.s1', '162.t1'], 'core': '648.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [26047, 18576, 2592, 36, 15552, 10368, 12096, 16056], 'label': '31104.fx.54.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '54.ba1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.ba1', 'subgroup_fusion': None, 'weyl_group': '864.4000'}
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id: 186247370
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.b1', '576.c1', '576.d1', '864.c1', '864.l1', '864.p1', '864.bd1', '864.bi1', '864.bn1', '864.bv1', '864.ce1', '864.cf1', '864.ct1', '864.df1'], 'contains': ['3456.a1', '5184.a1', '5184.b1', '5184.c1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [18144, 10368, 2016], 'label': '31104.fx.1728.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '1728.d1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247371
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.b1', '576.e1', '576.g1', '864.e1', '864.m1', '864.t1', '864.be1', '864.bj1', '864.bo1', '864.bs1', '864.cg1', '864.ci1', '864.cu1', '864.dg1'], 'contains': ['3456.i1', '5184.b1', '5184.d1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [18648, 12096, 12384], 'label': '31104.fx.1728.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '1728.e1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.e1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247372
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.b1', '576.f1', '576.h1', '864.d1', '864.n1', '864.bf1', '864.bk1', '864.bp1', '864.cv1', '864.dg1'], 'contains': ['3456.i1', '5184.b1', '5184.e1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [3096, 12096, 12384], 'label': '31104.fx.1728.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.k1', 'old_label': '1728.f1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.f1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
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id: 186247373
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.b1', '864.f1', '864.g1', '864.o1', '864.u1', '864.bg1', '864.bg2', '864.bl1', '864.bq1', '864.bq2', '864.bt1', '864.ch1', '864.cj1', '864.cu1', '864.cv1', '864.dh1'], 'contains': ['3456.i1', '5184.c1', '5184.d1', '5184.e1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [18144, 12096, 12384], 'label': '31104.fx.1728.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '1728.g1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.g1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247374
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.hr1', '576.c1', '864.i1', '864.v1', '864.ba1', '864.bw1', '864.ck1', '864.cl1', '864.di1'], 'contains': ['3456.j1', '5184.c1', '5184.f1', '5184.g1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [3096, 10924, 2016], 'label': '31104.fx.1728.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bj1', 'old_label': '1728.h1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.h1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247375
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.hs1', '576.c1', '576.e1', '576.f1', '864.j1', '864.w1', '864.bb1', '864.bx1', '864.cm1', '864.cn1', '864.dj1'], 'contains': ['3456.k1', '5184.b1', '5184.f1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [3096, 556, 12384], 'label': '31104.fx.1728.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.d1', 'old_label': '1728.i1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.i1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247376
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ht1', '576.c1', '576.g1', '576.h1', '864.by1', '864.co1', '864.do1'], 'contains': ['3456.m1', '5184.b1', '5184.g1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [3096, 10924, 12384], 'label': '31104.fx.1728.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.q1', 'old_label': '1728.j1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.j1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
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id: 186247377
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.hu1', '576.d1', '576.e1', '576.h1', '864.x1', '864.cp1', '864.dq1'], 'contains': ['3456.n2', '5184.b1', '5184.h1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [18144, 13780, 2016], 'label': '31104.fx.1728.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.i1', 'old_label': '1728.k1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.k1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247378
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.hv1', '576.d1', '576.f1', '576.g1', '576.h1', '864.dq1'], 'contains': ['3456.n2', '5184.b1', '5184.i1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [18216, 13780, 2016], 'label': '31104.fx.1728.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.g1', 'old_label': '1728.l1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.l1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
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id: 186247379
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.hw1', '576.d1', '864.y1', '864.cq1', '864.dr1'], 'contains': ['3456.n1', '5184.c1', '5184.h1', '5184.i1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [18144, 24148, 11764], 'label': '31104.fx.1728.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.bv1', 'old_label': '1728.m1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.m1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247380
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.m1', '18.s1', '27.d1'], 'contains': ['108.k1', '108.l1', '108.r1', '108.s1', '108.bd1', '108.be1', '108.bm1', '108.bn1', '108.du1', '108.ea1', '108.ei1', '162.t1', '162.u1'], 'core': '648.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [26047, 18576, 2592, 36, 15552, 22752, 12096, 16056], 'label': '31104.fx.54.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '54.bb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.bb1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
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id: 186247381
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.bs1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.i1', '864.a1', '864.cr1', '864.ef1', '864.ek1', '864.el1', '864.eo1', '864.er1', '864.et1', '864.ev1', '864.fa1', '864.ff1', '864.ff2', '864.fk1', '864.fn1', '864.fo1', '864.fq1', '864.fr1', '864.ft1', '864.fu1', '864.gb1', '864.gc1'], 'contains': ['3456.b1', '5184.j1', '5184.l1', '5184.m1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [16056, 12096, 22752], 'label': '31104.fx.1728.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '1728.n1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.n1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 186247382
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.i1', '864.a1', '864.b1', '864.cs1', '864.eg1', '864.em1', '864.ep1', '864.ew1', '864.ew2', '864.fb1', '864.fg1', '864.fg2', '864.fp1', '864.fs1', '864.gb1', '864.gd1'], 'contains': ['3456.b1', '5184.j1', '5184.m1', '5184.n1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [16056, 12096, 10368], 'label': '31104.fx.1728.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.s1', 'old_label': '1728.o1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.o1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 186247383
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.cm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.i1', '864.c1', '864.ct1', '864.eh1', '864.en1', '864.eq1', '864.es1', '864.ex1', '864.fc1', '864.fh1', '864.fm1', '864.fv1', '864.fw1', '864.fx1', '864.fy1', '864.gi1'], 'contains': ['3456.a1', '5184.j1', '5184.k1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [16056, 22752, 10368], 'label': '31104.fx.1728.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '1728.p1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.p1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 186247384
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.i1', '864.d1', '864.f1', '864.cu1', '864.ei1', '864.eu1', '864.ey1', '864.ey2', '864.fd1', '864.fi1', '864.fl1', '864.fz1', '864.ga1', '864.gj1'], 'contains': ['3456.i1', '5184.k1', '5184.l1', '5184.n1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [18576, 12096, 12384], 'label': '31104.fx.1728.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '1728.q1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.q1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 186247385
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.i1', '864.d1', '864.e1', '864.g1', '864.cv1', '864.ej1', '864.ez1', '864.ez2', '864.ez3', '864.fe1', '864.fj1', '864.gj1'], 'contains': ['3456.i1', '5184.k1', '5184.m1', '5184.n1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [16056, 12096, 12384], 'label': '31104.fx.1728.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1', 'old_label': '1728.r1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.r1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 186247386
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.s1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.eq1', '576.j1', '576.k1', '864.gm1', '864.gn1'], 'contains': ['3456.r1', '5184.o1', '5184.p1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [36, 30964, 16080], 'label': '31104.fx.1728.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.oi1', 'old_label': '1728.s1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.s1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247387
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ea1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.es1', '576.j1', '576.m1', '864.h1', '864.gs1'], 'contains': ['3456.c1', '5184.o1', '5184.q1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [36, 12940, 10368], 'label': '31104.fx.1728.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bg1', 'old_label': '1728.t1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.t1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247388
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.bv1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.et1', '432.lv1', '576.j1', '576.n1', '864.gp1', '864.gq1', '864.gt1'], 'contains': ['3456.d1', '5184.p1', '5184.q1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [36, 16080, 22752], 'label': '31104.fx.1728.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fx1', 'old_label': '1728.u1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.u1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247389
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.bk1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.eu1', '432.lw1', '576.j1', '576.l1', '576.n1', '864.go1', '864.gr1', '864.gu1'], 'contains': ['3456.e1', '5184.p1', '5184.q1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [36, 16080, 10368], 'label': '31104.fx.1728.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fx1', 'old_label': '1728.v1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.v1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247390
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ea1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ex1', '576.k1', '576.m1', '864.i1', '864.gv1'], 'contains': ['3456.j1', '5184.o1', '5184.r1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [36, 10924, 2016], 'label': '31104.fx.1728.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bi1', 'old_label': '1728.w1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.w1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247391
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.l1', '18.n1', '18.s1', '27.e1'], 'contains': ['108.m1', '108.u1', '108.bf1', '108.bo1', '108.dv1', '108.ee1', '108.eo1', '162.s1', '162.u1'], 'core': '216.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [19135, 18576, 2592, 36, 15552, 10368, 22752, 16056], 'label': '31104.fx.54.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '54.bc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.bc1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
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id: 186247392
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ea1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ey1', '576.k1', '576.m1', '576.o1', '864.j1', '864.gw1'], 'contains': ['3456.k1', '5184.o1', '5184.r1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [36, 556, 12384], 'label': '31104.fx.1728.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bh1', 'old_label': '1728.x1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.x1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247393
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.r1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.ez1', '432.fa1', '432.lx1', '576.k1', '576.n1', '864.gx1'], 'contains': ['3456.l1', '5184.p1', '5184.r1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 576, 'diagramx': None, 'generators': [36, 76, 12384], 'label': '31104.fx.1728.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.cx1', 'old_label': '1728.y1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.y1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 186247394
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.a1', '576.l1', '864.k1', '864.ef1', '864.eg1', '864.gy1', '864.gz1', '864.hc1'], 'contains': ['3456.b1', '5184.q1', '5184.s1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [36, 12096, 10368], 'label': '31104.fx.1728.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '576.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '1728.z1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.z1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
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id: 186247395
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.fk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.a1', '576.m1', '576.n1', '864.l1', '864.eh1', '864.ha1', '864.hb1'], 'contains': ['3456.a1', '5184.q1', '5184.r1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [36, 22752, 10368], 'label': '31104.fx.1728.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '576.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '1728.ba1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.ba1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 186247396
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.a1', '576.o1', '864.m1', '864.n1', '864.o1', '864.ei1', '864.ej1', '864.hd1'], 'contains': ['3456.i1', '5184.r1', '5184.s1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [36, 12096, 12384], 'label': '31104.fx.1728.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '576.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.r1', 'old_label': '1728.bb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.bb1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
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id: 186247397
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.me1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.p1', '576.r1', '864.ek1', '864.gy1', '864.he1', '864.hh1', '864.hq1'], 'contains': ['3456.b1', '5184.t1', '5184.u1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [12138, 12096, 22752], 'label': '31104.fx.1728.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.di1', 'old_label': '1728.bc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.bc1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247398
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.bd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.mf1', '576.p1', '576.q1', '576.s1', '864.go1', '864.hf1', '864.hw1'], 'contains': ['3456.e1', '5184.t1', '5184.v1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [17371, 5712, 10368], 'label': '31104.fx.1728.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fy1', 'old_label': '1728.bd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.bd1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247399
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.be1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.mg1', '576.p1', '576.t1', '864.hg1'], 'contains': ['3456.h1', '5184.t1', '5184.w1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 576, 'diagramx': None, 'generators': [17371, 29904, 10368], 'label': '31104.fx.1728.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.di1', 'old_label': '1728.be1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.be1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 186247400
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.mh1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.r1', '576.u1', '864.el1', '864.em1', '864.gz1', '864.hl1', '864.hl2', '864.hn1', '864.hq1'], 'contains': ['3456.b1', '5184.u1', '5184.x1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [12138, 12096, 10368], 'label': '31104.fx.1728.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.dl1', 'old_label': '1728.bf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.bf1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247401
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.bp1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.mj1', '576.q1', '576.x1', '864.gq1', '864.hi1', '864.hr1'], 'contains': ['3456.d1', '5184.t1', '5184.y1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [17371, 10368, 23836], 'label': '31104.fx.1728.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fx1', 'old_label': '1728.bg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.bg1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 186247402
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.o1', '18.p1', '18.t1', '27.e1'], 'contains': ['108.n1', '108.v1', '108.by1', '108.cg1', '108.cr1', '108.cw1', '108.cz1', '108.dm1', '108.dv1', '108.ex1', '108.fr1', '162.v1', '162.w1'], 'core': '216.b1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [1, 2592, 15552, 36, 18576, 10368, 22752, 16056], 'label': '31104.fx.54.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '54.bd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.bd1', 'subgroup_fusion': None, 'weyl_group': '288.977'}
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id: 186247403
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.bq1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.mm1', '576.s1', '576.v1', '864.gp1', '864.ho1', '864.hr1'], 'contains': ['3456.d1', '5184.v1', '5184.x1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [17371, 5712, 22752], 'label': '31104.fx.1728.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fz1', 'old_label': '1728.bh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.bh1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247404
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.mn1', '576.t1', '576.w1', '864.hp1'], 'contains': ['3456.h2', '5184.w1', '5184.x1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 576, 'diagramx': None, 'generators': [17371, 29904, 22752], 'label': '31104.fx.1728.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.dm1', 'old_label': '1728.bi1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.bi1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 186247405
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.fp1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.r1', '576.s1', '576.t1', '576.x1', '864.en1', '864.ha1', '864.hj1', '864.hm1', '864.hs1'], 'contains': ['3456.a1', '5184.t1', '5184.x1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [17371, 10368, 22752], 'label': '31104.fx.1728.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.x1', 'old_label': '1728.bj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.bj1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 186247406
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.v1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.ef1', '576.q1', '576.v1', '864.gm1', '864.hk1', '864.ht1'], 'contains': ['3456.r1', '5184.v1', '5184.y1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [17371, 8304, 23836], 'label': '31104.fx.1728.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fx1', 'old_label': '1728.bk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.bk1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 186247407
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.eg1', '576.q1', '576.v1', '864.hu1'], 'contains': ['3456.u1', '5184.v1', '5184.y1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 576, 'diagramx': None, 'generators': [17371, 18672, 23836], 'label': '31104.fx.1728.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.du1', 'old_label': '1728.bl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.bl1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247408
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.bm1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.mp1', '576.u1', '576.v1', '576.w1', '576.x1', '864.gr1', '864.hv1', '864.hw1'], 'contains': ['3456.e1', '5184.x1', '5184.y1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [17371, 23836, 22752], 'label': '31104.fx.1728.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.d1', 'old_label': '1728.bm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.bm1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
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id: 186247409
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.bn1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.mq1', '576.y1', '576.z1', '576.ba1', '864.gp1', '864.hi1', '864.ie1'], 'contains': ['3456.d1', '5184.z1', '5184.ba1', '5184.bb1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [26047, 5712, 22752], 'label': '31104.fx.1728.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.oj1', 'old_label': '1728.bn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.bn1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247410
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.ka1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.bb1', '576.bd1', '576.bj1', '864.eo1', '864.ep1', '864.gz1', '864.he1', '864.hl1', '864.hl2', '864.if1'], 'contains': ['3456.b1', '5184.z1', '5184.bd1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [6, 10368, 12096], 'label': '31104.fx.1728.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.gj1', 'old_label': '1728.bo1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.bo1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247411
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.bg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.mt1', '576.z1', '576.bb1', '576.bk1', '864.gr1', '864.hf1', '864.hx1'], 'contains': ['3456.e1', '5184.z1', '5184.be1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [6, 10368, 5712], 'label': '31104.fx.1728.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fx1', 'old_label': '1728.bp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.bp1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247412
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.bh1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.my1', '576.ba1', '576.bc1', '576.bg1', '576.bh1', '864.go1', '864.hv1', '864.hx1'], 'contains': ['3456.e1', '5184.ba1', '5184.bc1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [2670, 20812, 22752], 'label': '31104.fx.1728.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fz1', 'old_label': '1728.bq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.bq1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247413
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.q1', '18.t1', '27.d1'], 'contains': ['108.o1', '108.t1', '108.ca1', '108.ce1', '108.cs1', '108.cv1', '108.dd1', '108.dj1', '108.du1', '108.ey1', '108.fl1', '162.v1', '162.x1'], 'core': '648.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [20737, 2592, 15552, 36, 18576, 22752, 1728, 16056], 'label': '31104.fx.54.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '54.be1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.be1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
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id: 186247414
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.mu1', '576.y1', '576.bd1', '576.bk1', '864.hy1'], 'contains': ['3456.f1', '5184.z1', '5184.bf1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 576, 'diagramx': None, 'generators': [26047, 22752, 3100], 'label': '31104.fx.1728.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.dw1', 'old_label': '1728.br1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.br1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247415
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.mz1', '576.ba1', '576.be1', '576.bf1', '576.bi1', '864.hy1'], 'contains': ['3456.f1', '5184.bb1', '5184.bc1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 576, 'diagramx': None, 'generators': [2670, 76, 22752], 'label': '31104.fx.1728.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.dy1', 'old_label': '1728.bs1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.bs1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247416
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.mv1', '432.mv2', '576.bb1', '576.bd1', '576.bl1', '864.hg1'], 'contains': ['3456.h1', '5184.z1', '5184.bg1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 1728, 'diagramx': None, 'generators': [26047, 22752, 4540], 'label': '31104.fx.1728.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '864.hg1', 'old_label': '1728.bt1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.bt1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247417
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ni1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.ba1', '576.bj1', '576.bk1', '576.bl1', '864.eq1', '864.ha1', '864.hj1', '864.hm1', '864.hz1'], 'contains': ['3456.a1', '5184.z1', '5184.bc1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [6, 10368, 22752], 'label': '31104.fx.1728.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.dj1', 'old_label': '1728.bu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.bu1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247422
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.et1', '576.y1', '576.bf1', '864.id1'], 'contains': ['3456.v1', '5184.bb1', '5184.bf1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 576, 'diagramx': None, 'generators': [6, 28948, 28464], 'label': '31104.fx.1728.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.dw1', 'old_label': '1728.bz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.bz1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247423
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.kj1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.bc1', '576.be1', '576.bj1', '864.er1', '864.gy1', '864.hh1', '864.hn1', '864.if1'], 'contains': ['3456.b1', '5184.bc1', '5184.bd1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [6, 12096, 22752], 'label': '31104.fx.1728.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.x1', 'old_label': '1728.ca1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.ca1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
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id: 186247424
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.r1', '18.t1'], 'contains': ['108.p1', '108.w1', '108.cb1', '108.cf1', '108.ct1', '108.cu1', '108.cx1', '108.cy1', '108.de1', '108.df1', '108.dk1', '108.dl1', '108.dw1', '108.fe1', '108.fm1', '162.w1', '162.x1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [20737, 2592, 15552, 36, 18576, 12384, 1728, 16056], 'label': '31104.fx.54.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '54.bf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.bf1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186247425
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.cb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.nc1', '576.bf1', '576.bg1', '576.bk1', '864.gq1', '864.ho1', '864.ie1'], 'contains': ['3456.d1', '5184.bc1', '5184.be1', '5184.bf1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [26047, 3100, 10368], 'label': '31104.fx.1728.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bc1', 'old_label': '1728.cb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.cb1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186247426
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.nd1', '576.bh1', '576.bi1', '576.bl1', '864.hp1'], 'contains': ['3456.h2', '5184.bc1', '5184.bg1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [26047, 4540, 10368], 'label': '31104.fx.1728.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.x1', 'old_label': '1728.cc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.cc1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
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id: 186247427
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.di1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.bm1', '576.bn1', '576.bo1', '576.bp1', '576.bq1', '864.p1', '864.es1', '864.hb1', '864.hj1', '864.ig1', '864.ih1'], 'contains': ['3456.a1', '5184.bh1', '5184.bi1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [10405, 22752, 10368], 'label': '31104.fx.1728.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.d1', 'old_label': '1728.cd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.cd1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247428
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.dd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.bm1', '576.br1', '864.q1', '864.et1', '864.hc1', '864.he1', '864.hn1', '864.il1', '864.in1'], 'contains': ['3456.b1', '5184.bh1', '5184.bj1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [10405, 10368, 1728], 'label': '31104.fx.1728.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.c1', 'old_label': '1728.ce1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.ce1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247429
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.fi1', '576.bn1', '576.bs1', '864.r1', '864.gs1', '864.ii1'], 'contains': ['3456.c1', '5184.bh1', '5184.bk1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [10405, 10368, 12940], 'label': '31104.fx.1728.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.f1', 'old_label': '1728.cf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.cf1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247430
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.bu1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.fj1', '432.ni1', '576.bo1', '576.bs1', '864.gt1', '864.hi1', '864.ho1'], 'contains': ['3456.d1', '5184.bh1', '5184.bl1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [10405, 10368, 12460], 'label': '31104.fx.1728.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fz1', 'old_label': '1728.cg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.cg1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247431
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.bj1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.fk1', '432.nj1', '576.bo1', '576.br1', '576.bs1', '576.bt1', '864.gu1', '864.hf1', '864.hv1'], 'contains': ['3456.e1', '5184.bh1', '5184.bl1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [10405, 22752, 12460], 'label': '31104.fx.1728.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fz1', 'old_label': '1728.ch1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.ch1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247432
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.fm1', '576.bp1', '576.bt1', '864.s1'], 'contains': ['3456.g1', '5184.bh1', '5184.bm1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 576, 'diagramx': None, 'generators': [10405, 10368, 29404], 'label': '31104.fx.1728.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.h1', 'old_label': '1728.ci1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.ci1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247433
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.bj1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.fn1', '432.nk1', '576.bq1', '576.br1', '864.hg1'], 'contains': ['3456.h1', '5184.bh1', '5184.bn1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 576, 'diagramx': None, 'generators': [10405, 10368, 9168], 'label': '31104.fx.1728.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.dm1', 'old_label': '1728.cj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.cj1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247434
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.cj2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.fn2', '432.nk2', '576.bq1', '576.bt1', '864.hp1'], 'contains': ['3456.h2', '5184.bh1', '5184.bn1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 576, 'diagramx': None, 'generators': [10405, 22752, 9168], 'label': '31104.fx.1728.cj2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.dm1', 'old_label': '1728.cj2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.cj2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247435
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.u1', '18.w1', '27.d1'], 'contains': ['108.x1', '108.z1', '108.bp1', '108.cc1', '108.dx1', '108.ei1', '108.ey1', '162.y1', '162.z1'], 'core': '648.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [26485, 72, 2592, 12138, 22752, 12096, 18576, 15552], 'label': '31104.fx.54.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '54.bg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.bg1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
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id: 186247436
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.bm1', '576.bu1', '864.t1', '864.u1', '864.eu1', '864.hd1', '864.im1', '864.im2', '864.io1'], 'contains': ['3456.i1', '5184.bi1', '5184.bj1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [10405, 12384, 1728], 'label': '31104.fx.1728.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.f1', 'old_label': '1728.ck1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.ck1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247437
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.fs1', '576.bn1', '576.bw1', '864.v1', '864.gv1', '864.ij1'], 'contains': ['3456.j1', '5184.bi1', '5184.bk1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [10405, 2016, 12940], 'label': '31104.fx.1728.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.f1', 'old_label': '1728.cl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.cl1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247438
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ft1', '576.bn1', '576.bu1', '576.bv1', '576.bw1', '864.w1', '864.gw1', '864.ik1'], 'contains': ['3456.k1', '5184.bi1', '5184.bk1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [10405, 12384, 12940], 'label': '31104.fx.1728.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.f1', 'old_label': '1728.cm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.cm1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247439
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.fu1', '432.fv1', '432.nm1', '576.bo1', '576.bw1', '864.gx1'], 'contains': ['3456.l1', '5184.bi1', '5184.bl1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 576, 'diagramx': None, 'generators': [10405, 12384, 16080], 'label': '31104.fx.1728.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.dd1', 'old_label': '1728.cn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.cn1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247440
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.fy1', '576.bp1', '576.bv1', '864.y1'], 'contains': ['3456.n1', '5184.bi1', '5184.bm1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [10405, 12384, 29404], 'label': '31104.fx.1728.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.h1', 'old_label': '1728.co1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.co1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247441
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.co2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.fz1', '576.bp1', '576.bu1', '864.x1'], 'contains': ['3456.n2', '5184.bi1', '5184.bm1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [10405, 2016, 29404], 'label': '31104.fx.1728.co2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.h1', 'old_label': '1728.co2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.co2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247442
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.ga1', '432.gb1', '432.nn1', '576.bq1', '576.bv1'], 'contains': ['3456.o1', '5184.bi1', '5184.bn1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 1152, 'diagramx': None, 'generators': [10405, 12384, 24268], 'label': '31104.fx.1728.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '576.bq1', 'old_label': '1728.cp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.cp1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247443
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.gc1', '576.bs1', '576.bw1', '864.gn1', '864.hk1'], 'contains': ['3456.r1', '5184.bk1', '5184.bl1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [10405, 30964, 16080], 'label': '31104.fx.1728.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bc1', 'old_label': '1728.cq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.cq1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186247444
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ck1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.gd1', '576.bx1', '864.h1', '864.z1', '864.ii1'], 'contains': ['3456.c1', '5184.bo1', '5184.bp1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [3132, 21292, 22752], 'label': '31104.fx.1728.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.eb1', 'old_label': '1728.cr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.cr1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247445
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ck1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ge1', '576.bx1', '864.i1', '864.ba1', '864.ij1'], 'contains': ['3456.j1', '5184.bo1', '5184.bq1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [3132, 10924, 2016], 'label': '31104.fx.1728.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ef1', 'old_label': '1728.cs1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.cs1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247446
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '8.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1'], 'contains': ['16.a1', '16.b1', '16.c1', '24.c1', '24.d1', '24.e1', '24.f1', '32.c1'], 'core': '576.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [1, 15552, 12096, 22752, 36, 5712, 18648, 10368, 76], 'label': '31104.fx.8.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1', 'old_label': '8.b1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1', 'subgroup_fusion': None, 'weyl_group': None}
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id: 186247447
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.u1', '18.v1', '18.x1', '27.c1'], 'contains': ['108.dy1', '108.ej1', '108.fb1', '162.y1', '162.ba1', '216.kr1'], 'core': '216.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [26485, 2664, 18576, 12138, 28012, 15552, 2592, 22752], 'label': '31104.fx.54.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '54.bh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.bh1', 'subgroup_fusion': None, 'weyl_group': '384.17948'}
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id: 186247448
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ck1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.gf1', '576.bx1', '576.by1', '576.by2', '864.j1', '864.bb1', '864.ik1'], 'contains': ['3456.k1', '5184.bo1', '5184.bq2'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [3132, 556, 12384], 'label': '31104.fx.1728.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.eg1', 'old_label': '1728.ct1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.ct1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247449
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.bz1', '864.k1', '864.bc1', '864.bc2', '864.bh1', '864.ev1', '864.ew1', '864.ew2', '864.fa1', '864.fb1', '864.il1'], 'contains': ['3456.b1', '5184.bp1', '5184.br1', '5184.br2'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [18180, 12096, 22752], 'label': '31104.fx.1728.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.be1', 'old_label': '1728.cu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.cu1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186247450
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.ea1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.bx1', '576.bz1', '864.l1', '864.bd1', '864.bi1', '864.ex1', '864.fc1', '864.ig1'], 'contains': ['3456.a1', '5184.bp1', '5184.bq1', '5184.bq2'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [18180, 22752, 10368], 'label': '31104.fx.1728.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '1728.cv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.cv1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 186247451
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.by1', '576.bz1', '864.m1', '864.bg2', '864.bk1', '864.ez2', '864.fd1', '864.im1'], 'contains': ['3456.i1', '5184.bq2', '5184.br1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [18684, 12096, 12384], 'label': '31104.fx.1728.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.r1', 'old_label': '1728.cw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.cw1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
-
id: 186247452
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.cw2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.by2', '576.bz1', '864.n1', '864.bg1', '864.bj1', '864.bk1', '864.ey1', '864.ez1', '864.fe1'], 'contains': ['3456.i1', '5184.bq2', '5184.br2'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [15588, 12096, 12384], 'label': '31104.fx.1728.cw2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bp1', 'old_label': '1728.cw2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.cw2', 'subgroup_fusion': None, 'weyl_group': '54.5'}
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id: 186247453
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.cw3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.bz1', '864.o1', '864.be1', '864.bf1', '864.bl1', '864.ey2', '864.ez3', '864.fd1', '864.fe1', '864.im2'], 'contains': ['3456.i1', '5184.bq1', '5184.br1', '5184.br2'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [18252, 12096, 12384], 'label': '31104.fx.1728.cw3', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '1728.cw3', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.cw3', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186247454
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.ca1', '864.bc1', '864.bm1', '864.bm2', '864.eg1', '864.ev1', '864.ew2', '864.ff1', '864.fg1', '864.fg2', '864.hl2'], 'contains': ['3456.b1', '5184.bs1', '5184.bu1', '5184.bu2'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [16092, 12096, 10368], 'label': '31104.fx.1728.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bb1', 'old_label': '1728.cx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.cx1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186247455
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.cx2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.ca1', '864.bc2', '864.bm1', '864.ef1', '864.ew1', '864.ff2', '864.fg2', '864.hh1', '864.hl1', '864.in1'], 'contains': ['3456.b1', '5184.bs1', '5184.bu1', '5184.bu3'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [16092, 12096, 22752], 'label': '31104.fx.1728.cx2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '1728.cx2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.cx2', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186247456
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.bd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.ca1', '864.bd1', '864.bn1', '864.eh1', '864.ex1', '864.fh1', '864.hm1', '864.ih1'], 'contains': ['3456.a1', '5184.bs1', '5184.bt1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [16092, 22752, 10368], 'label': '31104.fx.1728.cy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '1728.cy1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.cy1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186247457
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.ca1', '864.be1', '864.bg2', '864.bp1', '864.bq1', '864.ei1', '864.ey2', '864.ez1', '864.fj1', '864.io1'], 'contains': ['3456.i1', '5184.bt1', '5184.bu2', '5184.bu3'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [540, 12096, 12384], 'label': '31104.fx.1728.cz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '1728.cz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.cz1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186247458
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.u1', '18.y1'], 'contains': ['108.dz1', '108.en1', '108.fd1', '162.y1', '162.bb1', '216.ks1'], 'core': '648.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13861, 16056, 432, 6, 19536, 15552, 2592, 10368], 'label': '31104.fx.54.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bi1', 'old_label': '54.bi1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.bi1', 'subgroup_fusion': None, 'weyl_group': '192.955'}
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id: 186247459
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.cz2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.ca1', '864.bf1', '864.bg1', '864.bo1', '864.bp1', '864.bq2', '864.ej1', '864.ey1', '864.ez2', '864.ez3', '864.fi1', '864.fj1'], 'contains': ['3456.i1', '5184.bt1', '5184.bu1', '5184.bu2'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [16092, 12096, 12384], 'label': '31104.fx.1728.cz2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.dw1', 'old_label': '1728.cz2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.cz2', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 186247460
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.ct1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.cb1', '576.cc1', '576.cd1', '864.br1', '864.fk1', '864.hc1', '864.hq1', '864.if1', '864.il1', '864.in1'], 'contains': ['3456.b1', '5184.bv1', '5184.bw1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1, 1728, 10368], 'label': '31104.fx.1728.da1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '1728.da1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.da1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247461
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.cd1', '576.ce1', '576.cf1', '864.bs1', '864.bt1', '864.fl1', '864.hd1', '864.im1', '864.im2', '864.io1'], 'contains': ['3456.i1', '5184.bv1', '5184.bx1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1, 1728, 12384], 'label': '31104.fx.1728.db1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.q1', 'old_label': '1728.db1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.db1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247462
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.go1', '576.cg1', '576.ch1', '576.ci1', '864.bu1', '864.gs1', '864.ii1'], 'contains': ['3456.c1', '5184.bw1', '5184.by1', '5184.ca1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [1, 10924, 10368], 'label': '31104.fx.1728.dc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.bd1', 'old_label': '1728.dc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.dc1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186247463
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.gp1', '432.nw1', '576.cg1', '576.ch1', '576.cj1', '864.gt1', '864.hr1', '864.ie1'], 'contains': ['3456.d1', '5184.bw1', '5184.bz1', '5184.cb1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [1, 76, 10368], 'label': '31104.fx.1728.dd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.oj1', 'old_label': '1728.dd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.dd1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186247464
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.gq1', '432.nx1', '576.cb1', '576.ch1', '576.cj1', '864.gu1', '864.hw1', '864.hx1'], 'contains': ['3456.e1', '5184.bw1', '5184.bz1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [1, 5712, 10368], 'label': '31104.fx.1728.de1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fy1', 'old_label': '1728.de1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.de1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
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id: 186247465
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.gr1', '432.ny1', '576.cc1', '576.cg1', '576.cj1', '864.hy1'], 'contains': ['3456.f1', '5184.bw1', '5184.cb1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 576, 'diagramx': None, 'generators': [1, 76, 22752], 'label': '31104.fx.1728.df1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.ea1', 'old_label': '1728.df1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.df1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
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id: 186247466
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.dc1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.cd1', '576.ci1', '576.cj1', '864.bv1', '864.fm1', '864.hb1', '864.hs1', '864.hz1', '864.ig1', '864.ih1'], 'contains': ['3456.a1', '5184.bw1', '5184.bx1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1, 22752, 10368], 'label': '31104.fx.1728.dg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.c1', 'old_label': '1728.dg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.dg1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186247467
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.gv1', '576.ci1', '576.ck1', '576.cl1', '864.bw1', '864.gv1', '864.ij1'], 'contains': ['3456.j1', '5184.bx1', '5184.by1', '5184.ca1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [1, 10924, 2016], 'label': '31104.fx.1728.dh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.be1', 'old_label': '1728.dh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.dh1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186247468
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.gw1', '576.ce1', '576.ci1', '576.cl1', '864.bx1', '864.gw1', '864.ik1'], 'contains': ['3456.k1', '5184.bx1', '5184.by1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [1, 556, 12384], 'label': '31104.fx.1728.di1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.g1', 'old_label': '1728.di1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.di1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
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id: 186247469
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.v1', '18.ba1', '27.b1'], 'contains': ['108.eb1', '108.eh1', '108.fa1', '162.y1', '162.bd1', '216.ku1'], 'core': '648.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [10405, 16056, 432, 12138, 16080, 15552, 2592, 22752], 'label': '31104.fx.54.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '54.bj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.bj1', 'subgroup_fusion': None, 'weyl_group': '384.17948'}
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id: 186247470
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.gx1', '432.gy1', '432.oa1', '576.cj1', '576.ck1', '576.cl1', '864.gx1'], 'contains': ['3456.l1', '5184.bx1', '5184.bz1', '5184.cb1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 1728, 'diagramx': None, 'generators': [1, 76, 12384], 'label': '31104.fx.1728.dj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '864.gx1', 'old_label': '1728.dj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.dj1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186247471
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ha1', '576.cf1', '576.ci1', '576.ck1', '864.by1'], 'contains': ['3456.m1', '5184.bx1', '5184.ca1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [1, 10924, 12384], 'label': '31104.fx.1728.dk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.r1', 'old_label': '1728.dk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.dk1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
-
id: 186247472
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.hb1', '432.hd1', '576.cg1', '576.ch1', '576.ck1', '576.cl1'], 'contains': ['3456.p1', '5184.by1', '5184.bz1', '5184.ca1', '5184.cb1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 3456, 'diagramx': None, 'generators': [1, 10228, 5712], 'label': '31104.fx.1728.dl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1728.dl1', 'old_label': '1728.dl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.dl1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 186247473
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.hc1', '432.he1', '576.cg1', '576.ck1', '576.cl1'], 'contains': ['3456.q1', '5184.by1', '5184.ca1', '5184.cb1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 1728, 'diagramx': None, 'generators': [1, 20596, 28464], 'label': '31104.fx.1728.dm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1728.dm1', 'old_label': '1728.dm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.dm1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 186247474
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.hf1', '576.ch1', '576.cl1', '864.gn1', '864.ht1', '864.ia1'], 'contains': ['3456.r1', '5184.by1', '5184.bz1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [1, 8212, 5712], 'label': '31104.fx.1728.dn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.oi1', 'old_label': '1728.dn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.dn1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186247475
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.hg1', '576.cg1', '576.cl1', '864.ib1'], 'contains': ['3456.s1', '5184.by1', '5184.cb1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [1, 18580, 28464], 'label': '31104.fx.1728.do1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '864.ib1', 'old_label': '1728.do1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.do1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186247476
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.hh1', '576.cg1', '576.ch1', '576.ck1', '864.ic1'], 'contains': ['3456.t1', '5184.bz1', '5184.ca1', '5184.cb1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 1728, 'diagramx': None, 'generators': [1, 18580, 5712], 'label': '31104.fx.1728.dp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '864.ic1', 'old_label': '1728.dp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.dp1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186247477
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.hi1', '576.ch1', '576.ck1', '864.hu1'], 'contains': ['3456.u1', '5184.bz1', '5184.ca1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [1, 30964, 5712], 'label': '31104.fx.1728.dq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '864.hu1', 'old_label': '1728.dq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.dq1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186247478
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.hj1', '576.cg1', '576.ck1'], 'contains': ['3456.v2', '5184.ca1', '5184.cb1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 1728, 'diagramx': None, 'generators': [1, 10228, 28464], 'label': '31104.fx.1728.dr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1728.dr1', 'old_label': '1728.dr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.dr1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 186247479
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1728.dr2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.hj2', '576.cg1', '576.ck1', '864.id1'], 'contains': ['3456.v1', '5184.ca1', '5184.cb1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [1, 28948, 28464], 'label': '31104.fx.1728.dr2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '864.id1', 'old_label': '1728.dr2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.dr2', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186247480
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.w1', '18.x1', '18.y1', '18.ba1', '27.e1'], 'contains': ['108.bb1', '108.bi1', '108.br1', '108.bz1', '108.ee1', '108.eo1', '108.ex1', '162.y1', '162.be1'], 'core': '216.b1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7477, 72, 2592, 6, 10368, 22752, 18576, 15552], 'label': '31104.fx.54.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '54.bk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.bk1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
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id: 186247481
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1', 'complements': ['16.d1'], 'conjugacy_class_count': 1, 'contained_in': ['648.a1', '648.fv1', '648.fw1', '648.fx1', '648.fy1', '648.fz1', '648.ga1', '648.gb1', '648.gc1', '972.ba1', '972.bb1', '972.bc1', '972.bd1', '972.be1'], 'contains': ['3888.y1', '3888.bd1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [16056, 18576, 18144, 15552], 'label': '31104.fx.1944.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1944.a1', 'normal_contained_in': ['648.a1'], 'normal_contains': ['31104.a1'], 'normalizer': '1.a1', 'old_label': '1944.a1', 'projective_image': '31104.fx', 'quotient_action_image': '36.10', 'quotient_action_kernel': '54.14', 'quotient_action_kernel_order': 54, 'quotient_fusion': None, 'short_label': '1944.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186247482
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.b1', '648.c1', '648.d1', '648.e1', '972.w1'], 'contains': ['3888.a1', '3888.b1', '3888.e1', '3888.f1', '3888.g1', '3888.j1', '3888.m1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [20737, 36, 16056], 'label': '31104.fx.1944.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.w1', 'old_label': '1944.b1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247483
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.f1', '648.g1', '648.h1', '648.i1', '972.w1'], 'contains': ['3888.b1', '3888.d1', '3888.e1', '3888.h1', '3888.i1', '3888.k1', '3888.l1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [20737, 2628, 16056], 'label': '31104.fx.1944.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.w1', 'old_label': '1944.c1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247484
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cj1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.j1', '648.k1', '648.l1', '648.m1', '972.a1', '972.b1', '972.e1'], 'contains': ['3888.n1', '3888.o1', '3888.p1', '3888.be1', '3888.bg1', '3888.bm1', '3888.bu1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [19135, 36, 18648], 'label': '31104.fx.1944.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '1944.d1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247485
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.n1', '648.o1', '648.p1', '972.a1', '972.f1', '972.w1'], 'contains': ['3888.f1', '3888.h1', '3888.n1', '3888.q1', '3888.t1', '3888.bf1', '3888.cb1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [20737, 36, 18144, 2592], 'label': '31104.fx.1944.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '1944.e1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.e1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
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id: 186247486
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.q1', '648.s1', '648.v1', '972.b1', '972.f1', '972.x1'], 'contains': ['3888.n1', '3888.u1', '3888.w1', '3888.bh1', '3888.ce1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [21169, 36, 18144], 'label': '31104.fx.1944.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '1944.f1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.f1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
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id: 186247487
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.r1', '648.t1', '648.u1', '648.w1', '972.h1', '972.w1', '972.x1'], 'contains': ['3888.g1', '3888.k1', '3888.n1', '3888.v1', '3888.x1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [5689, 36, 2592], 'label': '31104.fx.1944.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.h1', 'old_label': '1944.g1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.g1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247488
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.gb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.x1', '648.z1', '648.bh1', '972.a1', '972.c1', '972.i1'], 'contains': ['3888.o1', '3888.p1', '3888.q1', '3888.bi1', '3888.bl1', '3888.bt1', '3888.cd1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [26485, 12138, 18648], 'label': '31104.fx.1944.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '1944.h1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.h1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247489
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cm1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.ba1', '648.bb1', '648.bc1', '648.bg1', '972.c1', '972.d1', '972.e1'], 'contains': ['3888.o1', '3888.p1', '3888.s1', '3888.bj1', '3888.bn1', '3888.bv1', '3888.cg1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [19135, 2628, 18648], 'label': '31104.fx.1944.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '1944.i1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.i1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247490
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.gg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.y1', '648.bd1', '648.bi1', '972.b1', '972.d1', '972.i1'], 'contains': ['3888.o1', '3888.p1', '3888.u1', '3888.bk1', '3888.bq1', '3888.bx1', '3888.cj1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [10069, 6, 18648], 'label': '31104.fx.1944.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '1944.j1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.j1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 186247491
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.q1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.v1', '18.bc1', '27.a1'], 'contains': ['108.ef1', '108.ep1', '108.fk1', '162.ba1', '162.bd1', '864.hk1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [10405, 16056, 18576, 12138, 16080, 15552, 18144, 12460], 'label': '31104.fx.54.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '54.bl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.bl1', 'subgroup_fusion': None, 'weyl_group': '576.8654'}
-
id: 186247492
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.gd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.be1', '648.bj1', '972.a1', '972.d1', '972.m1'], 'contains': ['3888.o1', '3888.t1', '3888.bo1', '3888.br1', '3888.ch1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [5713, 12138, 18648], 'label': '31104.fx.1944.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '1944.k1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.k1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 186247493
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.gk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.bf1', '648.bk1', '972.b1', '972.c1', '972.m1'], 'contains': ['3888.o1', '3888.w1', '3888.bp1', '3888.bs1', '3888.ck1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [8305, 12138, 18648], 'label': '31104.fx.1944.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '1944.l1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.l1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247494
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.bl1', '648.bn1', '972.a1', '972.d1', '972.q1'], 'contains': ['3888.p1', '3888.t1', '3888.bw1', '3888.bz1', '3888.ci1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [5713, 6, 18648], 'label': '31104.fx.1944.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '1944.m1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.m1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247495
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.bm1', '648.bo1', '972.b1', '972.c1', '972.q1'], 'contains': ['3888.p1', '3888.w1', '3888.by1', '3888.ca1', '3888.cl1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [8305, 6, 18648], 'label': '31104.fx.1944.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '1944.n1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.n1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247496
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.bp1', '648.bq1', '648.bq2', '648.bt1', '972.r1', '972.w1', '972.y1'], 'contains': ['3888.i1', '3888.j1', '3888.q1', '3888.r1', '3888.x1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [5689, 16092, 2592], 'label': '31104.fx.1944.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.h1', 'old_label': '1944.o1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.o1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247497
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.br1', '648.bs1', '648.bu1', '972.c1', '972.f1', '972.y1'], 'contains': ['3888.q1', '3888.s1', '3888.w1', '3888.cc1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [21169, 468, 18144], 'label': '31104.fx.1944.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '1944.p1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.p1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
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id: 186247498
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.bv1', '648.bw1', '648.bx1', '648.by1', '972.t1', '972.w1', '972.z1'], 'contains': ['3888.l1', '3888.m1', '3888.r1', '3888.t1', '3888.v1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [20737, 16092, 2592], 'label': '31104.fx.1944.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.h1', 'old_label': '1944.q1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.q1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247499
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.bz1', '648.cb1', '648.cb2', '648.ce1', '972.r1', '972.x1', '972.z1'], 'contains': ['3888.r1', '3888.u1', '3888.x1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [5257, 16092], 'label': '31104.fx.1944.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.h1', 'old_label': '1944.r1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.r1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247500
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.ca1', '648.cc1', '648.cd1', '648.cf1', '972.t1', '972.x1', '972.y1'], 'contains': ['3888.r1', '3888.v1', '3888.w1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [21169, 16092], 'label': '31104.fx.1944.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.h1', 'old_label': '1944.s1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.s1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247501
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.cg1', '648.ch1', '648.ci1', '972.d1', '972.f1', '972.z1'], 'contains': ['3888.s1', '3888.t1', '3888.u1', '3888.cf1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [20737, 468, 18144], 'label': '31104.fx.1944.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '1944.t1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.t1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
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id: 186247502
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.w1', '18.bb1', '27.d1'], 'contains': ['108.bc1', '108.bg1', '108.bv1', '108.cd1', '108.ea1', '108.eu1', '108.ey1', '162.z1', '162.be1'], 'core': '648.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [26485, 2592, 18576, 12138, 72, 10368, 12096, 15552], 'label': '31104.fx.54.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '54.bm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.bm1', 'subgroup_fusion': None, 'weyl_group': '576.7160'}
-
id: 186247503
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.cj1', '648.ck1', '648.cl1', '648.cm1', '972.h1', '972.y1', '972.z1'], 'contains': ['3888.s1', '3888.v1', '3888.x1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [5689, 468], 'label': '31104.fx.1944.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.h1', 'old_label': '1944.u1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.u1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247504
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.cn1', '648.co1', '648.cp1', '648.cq1', '648.cr1', '972.e1', '972.f1', '972.g1', '972.h1', '972.ba1'], 'contains': ['3888.a1', '3888.c1', '3888.n1', '3888.s1', '3888.y1', '3888.cm1', '3888.cs1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [36, 18576, 18144, 16056], 'label': '31104.fx.1944.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '1944.v1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.v1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 186247505
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.lz1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.cs1', '648.ct1', '648.cu1', '648.cv1', '972.e1', '972.i1', '972.j1', '972.k1', '972.l1', '972.m1', '972.bb1'], 'contains': ['3888.o1', '3888.y1', '3888.cn1', '3888.co1', '3888.cu1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [17371, 16056, 2592], 'label': '31104.fx.1944.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '1944.w1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.w1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
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id: 186247506
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.jw1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.cw1', '648.cx1', '648.cy1', '648.cz1', '972.e1', '972.i1', '972.n1', '972.o1', '972.p1', '972.q1', '972.bc1'], 'contains': ['3888.p1', '3888.y1', '3888.cp1', '3888.cq1', '3888.cv1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [26047, 16056, 2592], 'label': '31104.fx.1944.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '1944.x1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.x1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 186247507
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.cx1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.da1', '648.db1', '648.dc1', '972.f1', '972.i1', '972.r1', '972.s1', '972.bd1'], 'contains': ['3888.q1', '3888.u1', '3888.y1', '3888.cr1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [10405, 18576, 18144], 'label': '31104.fx.1944.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '1944.y1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.y1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 186247508
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.dd1', '648.de1', '648.df1', '648.dg1', '648.dh1', '972.j1', '972.n1', '972.r1', '972.t1', '972.ba1'], 'contains': ['3888.c1', '3888.d1', '3888.r1', '3888.y1', '3888.cs1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [15588, 18576, 18144, 16056], 'label': '31104.fx.1944.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '1944.z1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.z1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 186247509
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.cp1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.di1', '648.dj1', '648.dk1', '972.f1', '972.m1', '972.q1', '972.t1', '972.u1', '972.v1', '972.be1'], 'contains': ['3888.t1', '3888.w1', '3888.y1', '3888.ct1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1, 18576, 18144], 'label': '31104.fx.1944.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '1944.ba1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.ba1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 186247510
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.lz1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.dl1', '648.dm1', '648.dt1', '648.du1', '972.g1', '972.l1', '972.n1', '972.o1', '972.s1', '972.u1', '972.bb1'], 'contains': ['3888.y1', '3888.cu1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [27690, 18144], 'label': '31104.fx.1944.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '1944.bb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bb1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 186247511
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.cx1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.dn1', '648.dr1', '648.dv1', '972.h1', '972.k1', '972.o1', '972.t1', '972.bd1'], 'contains': ['3888.v1', '3888.y1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [26461, 18576], 'label': '31104.fx.1944.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '1944.bc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bc1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 186247512
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.jw1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.do1', '648.dp1', '648.dw1', '648.dx1', '972.g1', '972.j1', '972.k1', '972.p1', '972.s1', '972.v1', '972.bc1'], 'contains': ['3888.y1', '3888.cv1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [15558, 18144], 'label': '31104.fx.1944.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '1944.bd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bd1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
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id: 186247513
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.x1', '18.bc1', '27.b1'], 'contains': ['108.ec1', '108.ev1', '108.fa1', '162.ba1', '162.be1', '216.lh1'], 'core': '648.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [12133, 16056, 432, 6, 22752, 15552, 2592, 5712], 'label': '31104.fx.54.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '54.bn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.bn1', 'subgroup_fusion': None, 'weyl_group': '1152.155790'}
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id: 186247514
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.cp1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.dq1', '648.ds1', '648.dy1', '972.h1', '972.l1', '972.p1', '972.r1', '972.be1'], 'contains': ['3888.x1', '3888.y1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [16057, 18576], 'label': '31104.fx.1944.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '1944.be1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.be1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
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id: 186247515
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.dz1', '648.ea1', '648.eb1', '648.ec1', '648.ed1', '648.ee1', '648.ef1', '972.w1'], 'contains': ['3888.f1', '3888.g1', '3888.i1', '3888.l1', '3888.z1', '3888.ba1', '3888.bc1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [20737, 36, 3096], 'label': '31104.fx.1944.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.w1', 'old_label': '1944.bf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bf1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247516
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.eg1', '648.eh1', '648.ei1', '648.ej1', '648.ek1', '972.w1'], 'contains': ['3888.h1', '3888.j1', '3888.k1', '3888.m1', '3888.ba1', '3888.bb1', '3888.bc1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [20737, 2628, 3096], 'label': '31104.fx.1944.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.w1', 'old_label': '1944.bg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bg1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247517
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.el1', '648.em1', '648.en1', '648.eo1', '648.ep1', '648.eq1', '972.w1', '972.x1', '972.ba1'], 'contains': ['3888.a1', '3888.d1', '3888.n1', '3888.r1', '3888.z1', '3888.bb1', '3888.bd1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [36, 16056, 3096, 15552], 'label': '31104.fx.1944.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.q1', 'old_label': '1944.bh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bh1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247518
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.cx1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.er1', '648.es1', '648.et1', '648.eu1', '648.ev1', '648.ew1', '972.w1', '972.y1', '972.bd1'], 'contains': ['3888.b1', '3888.q1', '3888.v1', '3888.ba1', '3888.bd1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [10405, 16056, 2592], 'label': '31104.fx.1944.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bd1', 'old_label': '1944.bi1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bi1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247519
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.ex1', '648.ey1', '648.ez1', '648.fa1', '648.fb1', '648.fc1', '972.y1', '972.z1', '972.ba1'], 'contains': ['3888.c1', '3888.r1', '3888.s1', '3888.bb1', '3888.bd1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [18612, 16056, 3096, 15552], 'label': '31104.fx.1944.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.q1', 'old_label': '1944.bj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bj1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247520
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.cp1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.fd1', '648.fe1', '648.ff1', '648.fg1', '648.fh1', '648.fi1', '972.w1', '972.z1', '972.be1'], 'contains': ['3888.e1', '3888.t1', '3888.x1', '3888.bc1', '3888.bd1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1, 16056, 2592], 'label': '31104.fx.1944.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '1944.bk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bk1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247521
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.cx1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.fj1', '648.fl1', '648.fm1', '648.fp1', '648.fr1', '648.fu1', '972.x1', '972.z1', '972.bd1'], 'contains': ['3888.u1', '3888.v1', '3888.bd1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [10837, 16056], 'label': '31104.fx.1944.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bd1', 'old_label': '1944.bl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bl1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247522
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.cp1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.fk1', '648.fn1', '648.fo1', '648.fq1', '648.fs1', '648.ft1', '972.x1', '972.y1', '972.be1'], 'contains': ['3888.w1', '3888.x1', '3888.bd1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [433, 16056], 'label': '31104.fx.1944.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '1944.bm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bm1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247523
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.bn1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.gd1', '648.ge1', '648.gj1', '972.a1', '972.bf1', '972.bg1'], 'contains': ['3888.be1', '3888.bf1', '3888.bg1', '3888.bl1', '3888.bo1', '3888.bt1', '3888.bw1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [5713, 21606, 36], 'label': '31104.fx.1944.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '1944.bn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bn1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247524
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.y1', '18.bd1'], 'contains': ['108.ed1', '108.ew1', '108.fd2', '162.bb1', '162.be1', '216.li1'], 'core': '648.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [26485, 2664, 18576, 12138, 10368, 15552, 2592, 29452], 'label': '31104.fx.54.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.y1', 'old_label': '54.bo1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.bo1', 'subgroup_fusion': None, 'weyl_group': '576.5126'}
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id: 186247525
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.bo1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.gf1', '648.gg1', '648.gk1', '972.b1', '972.bf1', '972.bg1'], 'contains': ['3888.be1', '3888.bg1', '3888.bh1', '3888.bp1', '3888.bq1', '3888.bx1', '3888.by1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [8305, 21678, 36], 'label': '31104.fx.1944.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '1944.bo1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bo1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247526
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.bp1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.gh1', '648.gl1', '972.a1', '972.bg1'], 'contains': ['3888.be1', '3888.bf1', '3888.bi1', '3888.br1', '3888.bz1', '3888.cw1', '3888.cx1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [5713, 24198, 36, 18576], 'label': '31104.fx.1944.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '1944.bp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bp1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247527
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.bq1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.gi1', '648.gm1', '972.b1', '972.bg1'], 'contains': ['3888.be1', '3888.bh1', '3888.bk1', '3888.bs1', '3888.ca1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [8305, 24198, 36], 'label': '31104.fx.1944.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '1944.bq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bq1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247528
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.gn1', '648.go1', '972.a1', '972.bf1'], 'contains': ['3888.bf1', '3888.bg1', '3888.cd1', '3888.ch1', '3888.ci1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [5713, 24270, 36], 'label': '31104.fx.1944.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '1944.br1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.br1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247529
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.bs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.gp1', '648.gq1', '972.b1', '972.bf1'], 'contains': ['3888.bg1', '3888.bh1', '3888.cj1', '3888.ck1', '3888.cl1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [8305, 24270, 36], 'label': '31104.fx.1944.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '1944.bs1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bs1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247530
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bf1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.gr1', '648.gt1', '648.hh1', '972.a1', '972.bh1', '972.bi1'], 'contains': ['3888.bi1', '3888.bm1', '3888.bo1', '3888.bu1', '3888.bw1', '3888.cb1', '3888.cd1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [5713, 21606, 108], 'label': '31104.fx.1944.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '1944.bt1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bt1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247531
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bh1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.gs1', '648.gu1', '648.hi1', '972.b1', '972.bh1', '972.bi1'], 'contains': ['3888.bk1', '3888.bm1', '3888.bp1', '3888.bu1', '3888.by1', '3888.ce1', '3888.cj1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [8305, 21606, 108], 'label': '31104.fx.1944.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '1944.bu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bu1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247532
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.be1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.gv1', '648.gx1', '648.hj1', '972.c1', '972.bg1', '972.bh1'], 'contains': ['3888.bi1', '3888.bj1', '3888.bp1', '3888.bt1', '3888.bv1', '3888.ca1', '3888.cc1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [8305, 24198, 2700], 'label': '31104.fx.1944.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '1944.bv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bv1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247533
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.be1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.gw1', '648.gy1', '648.hk1', '972.d1', '972.bg1', '972.bh1'], 'contains': ['3888.bj1', '3888.bk1', '3888.bo1', '3888.bv1', '3888.bx1', '3888.bz1', '3888.cf1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [5713, 24198, 2700], 'label': '31104.fx.1944.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '1944.bw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bw1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247534
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.gz1', '648.ha1', '648.hl1', '972.c1', '972.bf1', '972.bi1'], 'contains': ['3888.bl1', '3888.bn1', '3888.bp1', '3888.cc1', '3888.cd1', '3888.cg1', '3888.cl1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [8305, 24270, 2628], 'label': '31104.fx.1944.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '1944.bx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bx1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247535
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.z1', '18.be1', '27.d1'], 'contains': ['108.ba1', '108.bh1', '108.bk1', '108.ch1', '108.dx1', '108.ea1', '108.fl1', '162.bc1', '162.bf1'], 'core': '648.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [5713, 72, 2592, 12138, 12096, 22752, 18576, 15552], 'label': '31104.fx.54.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '54.bp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.bp1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
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id: 186247536
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.hb1', '648.hc1', '648.hm1', '972.d1', '972.bf1', '972.bi1'], 'contains': ['3888.bn1', '3888.bo1', '3888.bq1', '3888.cf1', '3888.cg1', '3888.ci1', '3888.cj1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [5713, 24270, 2628], 'label': '31104.fx.1944.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '1944.by1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.by1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247537
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.be1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.hd1', '648.hn1', '648.hp1', '972.c1', '972.bg1', '972.bi1'], 'contains': ['3888.bi1', '3888.bj1', '3888.bl1', '3888.bn1', '3888.bs1', '3888.by1', '3888.cc1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [8305, 21678, 2700], 'label': '31104.fx.1944.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '1944.bz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bz1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247538
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.be1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.he1', '648.ho1', '648.hq1', '972.d1', '972.bg1', '972.bi1'], 'contains': ['3888.bj1', '3888.bk1', '3888.bn1', '3888.bq1', '3888.br1', '3888.bw1', '3888.cf1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [5713, 21606, 2628], 'label': '31104.fx.1944.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '1944.ca1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.ca1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247539
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.hf1', '648.hr1', '972.a1', '972.bi1'], 'contains': ['3888.bl1', '3888.bm1', '3888.br1', '3888.cb1', '3888.ci1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [5713, 24270, 108], 'label': '31104.fx.1944.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '1944.cb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cb1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247540
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.hg1', '648.hs1', '972.b1', '972.bi1'], 'contains': ['3888.bm1', '3888.bq1', '3888.bs1', '3888.ce1', '3888.cl1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [8305, 24270, 108], 'label': '31104.fx.1944.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '1944.cc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cc1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247541
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.ht1', '648.hv1', '648.hw1', '972.c1', '972.bf1', '972.bh1'], 'contains': ['3888.bt1', '3888.bv1', '3888.by1', '3888.cc1', '3888.cd1', '3888.cg1', '3888.ck1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [8305, 21678, 2628], 'label': '31104.fx.1944.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '1944.cd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cd1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247542
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.hu1', '648.hx1', '648.hy1', '972.d1', '972.bf1', '972.bh1'], 'contains': ['3888.bv1', '3888.bw1', '3888.bx1', '3888.cf1', '3888.cg1', '3888.ch1', '3888.cj1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [5713, 21606, 2700], 'label': '31104.fx.1944.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '1944.ce1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.ce1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247543
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.hz1', '648.ib1', '972.a1', '972.bh1'], 'contains': ['3888.bt1', '3888.bu1', '3888.bz1', '3888.cb1', '3888.ch1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [5713, 24198, 108], 'label': '31104.fx.1944.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '1944.cf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cf1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247544
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.ia1', '648.ic1', '972.b1', '972.bh1'], 'contains': ['3888.bu1', '3888.bx1', '3888.ca1', '3888.ce1', '3888.ck1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [8305, 24198, 108], 'label': '31104.fx.1944.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '1944.cg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cg1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247545
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.ch1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.ie1', '648.ig1', '648.ih1', '648.ii1', '648.il1', '972.e1', '972.bf1', '972.bg1'], 'contains': ['3888.be1', '3888.bg1', '3888.bn1', '3888.bv1', '3888.cm1', '3888.cn1', '3888.cp1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [19135, 36, 16056], 'label': '31104.fx.1944.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '1944.ch1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.ch1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247546
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.bf1', '18.bg1', '27.b1'], 'contains': ['108.eb1', '108.ec1', '108.fo1', '162.bf1', '162.bg1', '216.ln1'], 'core': '648.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1, 16056, 432, 12138, 22752, 15552, 2592, 5712], 'label': '31104.fx.54.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '54.bq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.bq1', 'subgroup_fusion': None, 'weyl_group': '1152.155790'}
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id: 186247547
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.ci1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.id1', '648.ij1', '648.ik1', '648.im1', '972.e1', '972.bg1'], 'contains': ['3888.be1', '3888.bj1', '3888.cm1', '3888.co1', '3888.cq1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [19135, 36, 18576, 2592], 'label': '31104.fx.1944.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '1944.ci1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.ci1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186247548
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.if1', '648.in1', '648.in2', '648.io1', '648.ip1', '972.f1', '972.bf1', '972.bg1'], 'contains': ['3888.bf1', '3888.bh1', '3888.cc1', '3888.cf1', '3888.cm1', '3888.cr1', '3888.ct1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [20737, 36, 3024], 'label': '31104.fx.1944.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '1944.cj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cj1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247549
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.ck1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.iq1', '648.ir1', '648.is1', '648.it1', '972.e1', '972.g1', '972.bf1'], 'contains': ['3888.bg1', '3888.cg1', '3888.cm1', '3888.cu1', '3888.cv1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [6054, 36, 18576], 'label': '31104.fx.1944.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '1944.ck1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.ck1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
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id: 186247550
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cm1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.iv1', '648.iw1', '648.ix1', '648.jj1', '972.e1', '972.bh1', '972.bi1'], 'contains': ['3888.bj1', '3888.bm1', '3888.bu1', '3888.cg1', '3888.cn1', '3888.cp1', '3888.cs1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [19135, 2628, 16056], 'label': '31104.fx.1944.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '1944.cl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cl1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 186247551
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.ga1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.iu1', '648.iy1', '648.jk1', '648.jl1', '972.i1', '972.bg1', '972.bh1'], 'contains': ['3888.bi1', '3888.bk1', '3888.bt1', '3888.bx1', '3888.cn1', '3888.cq1', '3888.cr1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [26485, 12138, 2592], 'label': '31104.fx.1944.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '1944.cm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cm1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 186247552
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.gf1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.iz1', '648.ja1', '648.jm1', '972.i1', '972.bf1', '972.bi1'], 'contains': ['3888.bl1', '3888.bq1', '3888.cd1', '3888.cj1', '3888.cn1', '3888.cr1', '3888.cv1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [26485, 12210, 2592], 'label': '31104.fx.1944.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '1944.cn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cn1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247553
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.gi1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.jb1', '648.jc1', '648.jo1', '972.m1', '972.bf1', '972.bh1'], 'contains': ['3888.bo1', '3888.bp1', '3888.ch1', '3888.ck1', '3888.cn1', '3888.ct1', '3888.cu1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 12210, 2592], 'label': '31104.fx.1944.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '1944.co1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.co1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247554
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.fx1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.jd1', '648.je1', '648.jf1', '648.jg1', '648.jr1', '972.i1', '972.bg1', '972.bi1'], 'contains': ['3888.bi1', '3888.bk1', '3888.bl1', '3888.bq1', '3888.co1', '3888.cp1', '3888.cr1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [26485, 12138, 16056], 'label': '31104.fx.1944.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '1944.cp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cp1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247555
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cm1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.jh1', '648.ji1', '648.ji2', '648.js1', '972.e1', '972.j1', '972.bi1'], 'contains': ['3888.bm1', '3888.bn1', '3888.co1', '3888.cs1', '3888.cv1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [6054, 18180, 18576], 'label': '31104.fx.1944.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '1944.cq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cq1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
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id: 186247556
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.fy1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.jn1', '648.jp1', '648.jq1', '648.jt1', '972.m1', '972.bg1', '972.bi1'], 'contains': ['3888.bo1', '3888.bp1', '3888.br1', '3888.bs1', '3888.cn1', '3888.co1', '3888.ct1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 12138, 2592], 'label': '31104.fx.1944.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '1944.cr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cr1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247557
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': ['15552.e1', '15552.d1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.d1', '4.e1', '6.d1', '6.f1', '6.g1', '8.b1'], 'core': '2.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 15984, 12096, 22752, 18144, 36, 5712, 15624, 10368, 15552, 76], 'label': '31104.fx.2.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.d1', '4.e1'], 'normalizer': '1.a1', 'old_label': '2.b1', 'projective_image': '31104.fx', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1', 'subgroup_fusion': None, 'weyl_group': '31104.fx'}
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id: 186247558
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '9.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3.a1'], 'contains': ['18.g1', '18.h1', '18.i1', '18.v1', '18.bc1', '18.bf1', '18.bi1', '27.a1', '27.b1', '27.c1', '144.fx1'], 'core': '108.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1, 18144, 16080, 10368, 15552, 24198, 22828, 18576, 16056, 36], 'label': '31104.fx.9.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '9.a1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.a1', 'subgroup_fusion': None, 'weyl_group': '3456.di'}
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id: 186247559
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.z1', '18.bg1', '27.e1'], 'contains': ['108.bj1', '108.bl1', '108.cj1', '108.ee1', '108.fr1', '162.bf1'], 'core': '216.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [5713, 2592, 18576, 12138, 72, 10368, 22752, 15552], 'label': '31104.fx.54.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '54.br1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.br1', 'subgroup_fusion': None, 'weyl_group': '576.7160'}
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id: 186247560
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.ge1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.ju1', '648.jx1', '648.jy1', '972.i1', '972.bf1', '972.bh1'], 'contains': ['3888.bt1', '3888.bx1', '3888.cd1', '3888.cj1', '3888.cp1', '3888.cr1', '3888.cu1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [26485, 14730, 16056], 'label': '31104.fx.1944.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '1944.cs1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cs1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247561
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.jv1', '648.jz1', '648.ka1', '972.q1', '972.bf1', '972.bi1'], 'contains': ['3888.bw1', '3888.by1', '3888.ci1', '3888.cl1', '3888.cp1', '3888.ct1', '3888.cv1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [5713, 78, 2592], 'label': '31104.fx.1944.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '1944.ct1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.ct1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247562
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cm1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.jw1', '648.ke1', '648.kf1', '648.kg1', '972.e1', '972.n1', '972.bh1'], 'contains': ['3888.bu1', '3888.bv1', '3888.cq1', '3888.cs1', '3888.cu1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [19135, 16092, 2592], 'label': '31104.fx.1944.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '1944.cu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cu1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
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id: 186247563
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.be1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.kb1', '648.kc1', '648.kd1', '648.kh1', '648.ki1', '972.q1', '972.bg1', '972.bh1'], 'contains': ['3888.bw1', '3888.by1', '3888.bz1', '3888.ca1', '3888.cp1', '3888.cq1', '3888.ct1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [5713, 6, 2592], 'label': '31104.fx.1944.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '1944.cv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cv1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247564
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.n1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.kj1', '648.kj2', '648.kk1', '648.kl1', '972.f1', '972.bh1', '972.bi1'], 'contains': ['3888.cb1', '3888.cc1', '3888.ce1', '3888.cf1', '3888.cr1', '3888.cs1', '3888.ct1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [20737, 15588, 3024], 'label': '31104.fx.1944.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '1944.cw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cw1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247565
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '1944.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cm1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.km1', '648.kn1', '648.ko1', '648.kp1', '648.kp2', '972.g1', '972.j1', '972.n1'], 'contains': ['3888.cs1', '3888.cu1', '3888.cv1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [3583, 16092], 'label': '31104.fx.1944.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.g1', 'old_label': '1944.cx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cx1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 186247566
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.a1', '864.b1', '864.c1', '1296.a1', '1296.h1', '1296.l1', '1296.s1', '1296.ba1', '1296.ed1', '1296.fo1'], 'contains': ['5184.a1', '5184.j1', '7776.a1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [16056, 15552, 10368], 'label': '31104.fx.2592.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '2592.a1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247567
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.c1', '864.d1', '864.e1', '1296.b1', '1296.i1', '1296.m1', '1296.t1', '1296.bb1', '1296.ee1', '1296.fq1'], 'contains': ['5184.b1', '5184.k1', '7776.a1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [16056, 15552, 12384], 'label': '31104.fx.2592.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '2592.b1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247568
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.c1', '864.f1', '864.g1', '1296.c1', '1296.j1', '1296.n1', '1296.u1', '1296.bc1', '1296.ee1', '1296.fp1'], 'contains': ['5184.c1', '5184.k1', '7776.a1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [3024, 18216, 12384], 'label': '31104.fx.2592.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '2592.c1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247569
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.a1', '864.d1', '864.f1', '1296.d1', '1296.o1', '1296.v1', '1296.eg1', '1296.fr1'], 'contains': ['5184.e1', '5184.l1', '5184.n1', '7776.a1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [18144, 18576, 12096], 'label': '31104.fx.2592.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1', 'old_label': '2592.d1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247570
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bf1', '27.a1'], 'contains': ['108.ef1', '108.fy1', '162.bg1', '864.ht1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [1, 16056, 18576, 12138, 5712, 15552, 18144, 20812], 'label': '31104.fx.54.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.bs1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.bs1', 'subgroup_fusion': None, 'weyl_group': '576.8654'}
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id: 186247571
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.a1', '864.e1', '864.g1', '1296.e1', '1296.p1', '1296.p2', '1296.w1', '1296.ef1', '1296.eh1', '1296.fs1'], 'contains': ['5184.d1', '5184.m1', '7776.a1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [16056, 2592, 12096], 'label': '31104.fx.2592.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1', 'old_label': '2592.e1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247572
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.b1', '864.e1', '864.f1', '1296.f1', '1296.k1', '1296.q1', '1296.x1', '1296.z1', '1296.eh1', '1296.fr1'], 'contains': ['5184.d1', '5184.n1', '7776.a1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [432, 72, 12096], 'label': '31104.fx.2592.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '2592.f1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.f1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247573
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.a1', '864.b1', '864.d1', '864.g1', '1296.g1', '1296.r1', '1296.r2', '1296.y1', '1296.eg1', '1296.eh1', '1296.fs1'], 'contains': ['5184.e1', '5184.m1', '5184.n1', '7776.a1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [504, 2592, 12096], 'label': '31104.fx.2592.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1', 'old_label': '2592.g1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247574
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.el1', '864.h1', '864.i1', '864.j1', '1296.bd1', '1296.be1', '1296.ei1'], 'contains': ['5184.f1', '5184.o1', '5184.bo1', '7776.b1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [36, 3096, 12940], 'label': '31104.fx.2592.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.dz1', 'old_label': '2592.h1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.h1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247575
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.ea1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.h1', '864.k1', '864.l1', '1296.a1', '1296.bf1', '1296.bj1', '1296.cn1', '1296.el1'], 'contains': ['5184.a1', '5184.q1', '5184.bp1', '7776.b1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [36, 18144, 22752], 'label': '31104.fx.2592.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.u1', 'old_label': '2592.i1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.i1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247576
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.ea1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.j1', '864.l1', '864.m1', '864.n1', '1296.b1', '1296.bg1', '1296.bk1', '1296.co1', '1296.em1'], 'contains': ['5184.b1', '5184.r1', '5184.bq2', '7776.b1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [36, 3096, 12384], 'label': '31104.fx.2592.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.y1', 'old_label': '2592.j1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.j1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247577
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.ea1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.i1', '864.l1', '864.o1', '1296.c1', '1296.bh1', '1296.bl1', '1296.co1', '1296.en1'], 'contains': ['5184.c1', '5184.r1', '5184.bq1', '7776.b1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [36, 18144, 12384], 'label': '31104.fx.2592.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '2592.k1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.k1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247578
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.k1', '864.m1', '864.o1', '1296.e1', '1296.f1', '1296.bi1', '1296.bm1', '1296.cp1', '1296.cq1', '1296.eo1'], 'contains': ['5184.d1', '5184.s1', '5184.br1', '7776.b1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [36, 18648, 12096], 'label': '31104.fx.2592.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '2592.l1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.l1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247579
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.k1', '864.n1', '864.o1', '1296.d1', '1296.g1', '1296.cq1', '1296.cr1', '1296.eo1'], 'contains': ['5184.e1', '5184.s1', '5184.br2', '7776.b1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [36, 18144, 12096], 'label': '31104.fx.2592.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.di1', 'old_label': '2592.m1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.m1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247580
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.di1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.p1', '864.q1', '864.r1', '864.s1', '1296.h1', '1296.bf1', '1296.bn1', '1296.bq1', '1296.bt1', '1296.da1', '1296.ep1'], 'contains': ['5184.a1', '5184.bh1', '7776.c1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [10405, 18144, 10368], 'label': '31104.fx.2592.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cr1', 'old_label': '2592.n1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.n1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247581
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bf1'], 'contains': ['108.eg1', '108.gb1', '162.bg1', '864.hu1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1, 16056, 18576, 22506, 16080, 15552, 18144, 20812], 'label': '31104.fx.54.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bt1', 'old_label': '54.bt1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.bt1', 'subgroup_fusion': None, 'weyl_group': '576.8654'}
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id: 186247582
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.di1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.p1', '864.t1', '864.w1', '864.x1', '1296.i1', '1296.bg1', '1296.bo1', '1296.br1', '1296.bu1', '1296.db1', '1296.eq1'], 'contains': ['5184.b1', '5184.bi1', '7776.c1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [10405, 15552, 12384], 'label': '31104.fx.2592.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cr1', 'old_label': '2592.o1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.o1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247583
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.di1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.p1', '864.u1', '864.v1', '864.y1', '1296.j1', '1296.bh1', '1296.bp1', '1296.bs1', '1296.bv1', '1296.db1', '1296.er1'], 'contains': ['5184.c1', '5184.bi1', '7776.c1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [10405, 18144, 12384], 'label': '31104.fx.2592.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cr1', 'old_label': '2592.p1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.p1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247584
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.dx1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.q1', '864.t1', '864.u1', '1296.k1', '1296.bi1', '1296.bx1', '1296.by1', '1296.bz1', '1296.dc1', '1296.es1'], 'contains': ['5184.d1', '5184.bj1', '7776.c1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [10405, 18144, 1728], 'label': '31104.fx.2592.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bc1', 'old_label': '2592.q1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.q1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247585
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.ev1', '864.r1', '864.v1', '864.w1', '1296.bd1', '1296.bw1', '1296.et1'], 'contains': ['5184.f1', '5184.bk1', '7776.c1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [10405, 15552, 12940], 'label': '31104.fx.2592.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bj1', 'old_label': '2592.r1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.r1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247586
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.ew1', '864.s1', '864.x1', '864.y1', '1296.ew1'], 'contains': ['5184.h1', '5184.bm1', '7776.c1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [10405, 18144, 29404], 'label': '31104.fx.2592.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.bv1', 'old_label': '2592.s1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.s1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247587
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.ex1', '864.z1', '864.ba1', '864.bb1', '1296.bw1', '1296.ca1', '1296.ei1'], 'contains': ['5184.f1', '5184.bo1', '7776.e1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [15588, 3096, 12940], 'label': '31104.fx.2592.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.dz1', 'old_label': '2592.t1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.t1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247588
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.bd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.bc1', '864.bc2', '864.bd1', '1296.l1', '1296.s1', '1296.bn1', '1296.cb1', '1296.cn1', '1296.dd1', '1296.fa1'], 'contains': ['5184.a1', '5184.bp1', '5184.bs1', '7776.d1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [3132, 18144, 22752], 'label': '31104.fx.2592.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.v1', 'old_label': '2592.u1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.u1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247589
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.bd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.bd1', '864.be1', '864.bf1', '1296.m1', '1296.t1', '1296.bo1', '1296.cc1', '1296.co1', '1296.de1', '1296.fb1'], 'contains': ['5184.b1', '5184.bq1', '5184.bt1', '7776.d1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [108, 3096, 12384], 'label': '31104.fx.2592.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.w1', 'old_label': '2592.v1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.v1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247590
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.bd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.bd1', '864.bg1', '864.bg2', '1296.n1', '1296.u1', '1296.bp1', '1296.cd1', '1296.co1', '1296.de2', '1296.fc1'], 'contains': ['5184.c1', '5184.bq2', '5184.bt1', '7776.d1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [3132, 18144, 12384], 'label': '31104.fx.2592.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.w1', 'old_label': '2592.w1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.w1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247591
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.bc1', '864.be1', '864.bg1', '1296.p1', '1296.q1', '1296.w1', '1296.cq1', '1296.df1', '1296.dg1', '1296.fd2'], 'contains': ['5184.d1', '5184.br2', '5184.bu2', '7776.d1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [18180, 18648, 12096], 'label': '31104.fx.2592.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.di1', 'old_label': '2592.x1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.x1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247592
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.ba1', '18.bb1', '18.bc1', '18.bd1', '27.c1'], 'contains': ['108.a1', '108.ek1', '108.fb1', '162.bd1', '162.be1', '216.lm1'], 'core': '108.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7477, 2664, 18576, 6, 22752, 15552, 2592, 5260], 'label': '31104.fx.54.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '54.bu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.bu1', 'subgroup_fusion': None, 'weyl_group': '1152.155790'}
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id: 186247593
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.x2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.bc2', '864.be1', '864.bg2', '1296.p2', '1296.x1', '1296.bx1', '1296.ce1', '1296.cp1', '1296.dg1', '1296.fd1'], 'contains': ['5184.d1', '5184.br1', '5184.bu3', '7776.d1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [18612, 18648, 12096], 'label': '31104.fx.2592.x2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '2592.x2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.x2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 186247594
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.bc1', '864.bc2', '864.bf1', '864.bg1', '1296.o1', '1296.r2', '1296.y1', '1296.cr1', '1296.dg2', '1296.dh1', '1296.fd2'], 'contains': ['5184.e1', '5184.br2', '5184.bu1', '7776.d1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [2628, 18144, 12096], 'label': '31104.fx.2592.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.di1', 'old_label': '2592.y1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.y1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247595
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.y2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.bc1', '864.bf1', '864.bg2', '1296.r1', '1296.v1', '1296.cq1', '1296.dh1', '1296.fd1'], 'contains': ['5184.e1', '5184.br1', '5184.bu2', '7776.d1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [18684, 18144, 12096], 'label': '31104.fx.2592.y2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.di1', 'old_label': '2592.y2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.y2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247596
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.fx1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.z1', '864.bh1', '864.bi1', '1296.s1', '1296.bq1', '1296.cg1', '1296.dd1', '1296.el1'], 'contains': ['5184.a1', '5184.bp1', '7776.e1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [108, 18144, 10368], 'label': '31104.fx.2592.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.u1', 'old_label': '2592.z1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.z1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247597
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.fx1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.bb1', '864.bi1', '864.bj1', '864.bk1', '1296.t1', '1296.br1', '1296.ch1', '1296.de2', '1296.em1'], 'contains': ['5184.b1', '5184.bq2', '7776.e1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [15588, 3096, 12384], 'label': '31104.fx.2592.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.y1', 'old_label': '2592.ba1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.ba1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247598
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.fx1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.ba1', '864.bi1', '864.bl1', '1296.u1', '1296.bs1', '1296.ci1', '1296.de1', '1296.en1'], 'contains': ['5184.c1', '5184.bq1', '7776.e1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [18252, 18144, 12384], 'label': '31104.fx.2592.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '2592.bb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.bb1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247599
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.bh1', '864.bj1', '864.bl1', '1296.w1', '1296.x1', '1296.by1', '1296.cf1', '1296.df1', '1296.dg2', '1296.eo1'], 'contains': ['5184.d1', '5184.br2', '7776.e1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [15588, 18648, 12096], 'label': '31104.fx.2592.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '2592.bc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.bc1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 186247600
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.bh1', '864.bk1', '864.bl1', '1296.v1', '1296.y1', '1296.dg1', '1296.dh1', '1296.eo1'], 'contains': ['5184.e1', '5184.br1', '5184.br2', '7776.e1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [108, 18144, 12096], 'label': '31104.fx.2592.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.di1', 'old_label': '2592.bd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.bd1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 186247601
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.bm1', '864.bm2', '864.bn1', '1296.a1', '1296.l1', '1296.bt1', '1296.ck1', '1296.dd1', '1296.di1', '1296.fa1'], 'contains': ['5184.a1', '5184.bs1', '7776.f1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [18612, 18144, 22752], 'label': '31104.fx.2592.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.v1', 'old_label': '2592.be1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.be1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 186247602
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.bn1', '864.bo1', '864.bp1', '1296.b1', '1296.m1', '1296.bu1', '1296.cl1', '1296.de2', '1296.dj1', '1296.fb1'], 'contains': ['5184.b1', '5184.bt1', '7776.f1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [15660, 3096, 12384], 'label': '31104.fx.2592.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.w1', 'old_label': '2592.bf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.bf1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247603
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.be1', '18.bf1', '18.bg1', '27.c1'], 'contains': ['108.a1', '108.dy1', '108.fp1', '162.bf1', '162.bg1', '216.lp1'], 'core': '108.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1, 16056, 432, 12138, 10368, 15552, 2592, 5712], 'label': '31104.fx.54.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '54.bv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.bv1', 'subgroup_fusion': None, 'weyl_group': '3456.gu'}
-
id: 186247604
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.bn1', '864.bq1', '864.bq2', '1296.c1', '1296.n1', '1296.bv1', '1296.cm1', '1296.de1', '1296.dj1', '1296.fc1'], 'contains': ['5184.c1', '5184.bt1', '7776.f1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [468, 18144, 12384], 'label': '31104.fx.2592.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.w1', 'old_label': '2592.bg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.bg1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 186247605
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.bm1', '864.bo1', '864.bq2', '1296.e1', '1296.p2', '1296.q1', '1296.dg2', '1296.dk1', '1296.dl1', '1296.fd2'], 'contains': ['5184.d1', '5184.bu1', '7776.f1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [2628, 18648, 12096], 'label': '31104.fx.2592.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.di1', 'old_label': '2592.bh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.bh1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 186247606
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.bh2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.bm2', '864.bo1', '864.bq1', '1296.f1', '1296.p1', '1296.bz1', '1296.cj1', '1296.df1', '1296.dl1', '1296.fd1'], 'contains': ['5184.d1', '5184.bu2', '7776.f1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [3060, 18648, 12096], 'label': '31104.fx.2592.bh2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '2592.bh2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.bh2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 186247607
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.bm1', '864.bm2', '864.bp1', '864.bq2', '1296.g1', '1296.o1', '1296.r1', '1296.dh1', '1296.dl1', '1296.dm1', '1296.fd2'], 'contains': ['5184.e1', '5184.bu1', '5184.bu2', '7776.f1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [16020, 18144, 12096], 'label': '31104.fx.2592.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.di1', 'old_label': '2592.bi1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.bi1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 186247608
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.bi2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.bm1', '864.bp1', '864.bq1', '1296.d1', '1296.r2', '1296.dg1', '1296.dm1', '1296.fd1'], 'contains': ['5184.e1', '5184.bu2', '5184.bu3', '7776.f1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [18612, 18144, 12096], 'label': '31104.fx.2592.bi2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.di1', 'old_label': '2592.bi2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.bi2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 186247609
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.dn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.br1', '864.bs1', '864.bt1', '1296.z1', '1296.bi1', '1296.bx1', '1296.cf1', '1296.cj1', '1296.dn1', '1296.fe1'], 'contains': ['5184.d1', '5184.bv1', '7776.g1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1, 18144, 1728], 'label': '31104.fx.2592.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cp1', 'old_label': '2592.bj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.bj1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247610
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.dc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.br1', '864.bu1', '864.bv1', '1296.ba1', '1296.bf1', '1296.bn1', '1296.cg1', '1296.ck1', '1296.do1', '1296.ff1'], 'contains': ['5184.a1', '5184.bw1', '7776.g1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1, 18144, 10368], 'label': '31104.fx.2592.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cs1', 'old_label': '2592.bk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.bk1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247611
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.dc1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.bs1', '864.bv1', '864.bx1', '864.by1', '1296.bb1', '1296.bg1', '1296.bo1', '1296.ch1', '1296.cl1', '1296.dp1', '1296.fg1'], 'contains': ['5184.b1', '5184.bx1', '7776.g1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1, 15552, 12384], 'label': '31104.fx.2592.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cu1', 'old_label': '2592.bl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.bl1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247612
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.dc1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.bt1', '864.bv1', '864.bw1', '1296.bc1', '1296.bh1', '1296.bp1', '1296.ci1', '1296.cm1', '1296.dp1', '1296.fh1'], 'contains': ['5184.c1', '5184.bx1', '7776.g1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1, 18144, 12384], 'label': '31104.fx.2592.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ct1', 'old_label': '2592.bm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.bm1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247613
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.fh1', '864.bu1', '864.bw1', '864.bx1', '1296.bd1', '1296.ca1', '1296.fi1'], 'contains': ['5184.f1', '5184.by1', '7776.g1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [1, 15552, 556], 'label': '31104.fx.2592.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.dz1', 'old_label': '2592.bn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.bn1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247614
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.bi1', '18.bj1', '18.bk1', '27.c1'], 'contains': ['108.ej1', '108.ek1', '108.fp1', '162.bh1', '162.bi1', '216.lz1'], 'core': '216.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [5713, 2664, 18576, 6, 22752, 15552, 2592, 5260], 'label': '31104.fx.54.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '54.bw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.bw1', 'subgroup_fusion': None, 'weyl_group': '1152.155790'}
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id: 186247615
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.fi1', '864.bu1', '864.bw1', '864.by1', '1296.fl1'], 'contains': ['5184.g1', '5184.ca1', '7776.g1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [1, 15552, 10924], 'label': '31104.fx.2592.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1296.fl1', 'old_label': '2592.bo1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.bo1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247616
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ed1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.bz1', '864.cb1', '864.cd1', '864.ce1', '1296.h1', '1296.bj1', '1296.cb1', '1296.cg1', '1296.ck1', '1296.dr1', '1296.ep1'], 'contains': ['5184.a1', '7776.h1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [26029, 10368, 18144], 'label': '31104.fx.2592.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cr1', 'old_label': '2592.bp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.bp1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247617
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.ea1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.ca1', '864.cc1', '864.cf1', '1296.ba1', '1296.bj1', '1296.bq1', '1296.bt1', '1296.cb1', '1296.dt1', '1296.ff1'], 'contains': ['5184.a1', '7776.i1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [15625, 18144, 10368], 'label': '31104.fx.2592.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cs1', 'old_label': '2592.bq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.bq1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247618
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ed1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.ce1', '864.cg1', '864.cm1', '864.cp1', '1296.i1', '1296.bk1', '1296.cc1', '1296.ch1', '1296.cl1', '1296.dv1', '1296.eq1'], 'contains': ['5184.b1', '7776.h1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26461, 12384, 15552], 'label': '31104.fx.2592.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cr1', 'old_label': '2592.br1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.br1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247619
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ed1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.ce1', '864.ch1', '864.ck1', '864.cq1', '1296.j1', '1296.bl1', '1296.cd1', '1296.ci1', '1296.cm1', '1296.dw1', '1296.er1'], 'contains': ['5184.c1', '7776.h1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13069, 12384, 18144], 'label': '31104.fx.2592.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cr1', 'old_label': '2592.bs1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.bs1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247620
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.ea1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.cf1', '864.ci1', '864.cn1', '864.co1', '1296.bb1', '1296.bk1', '1296.br1', '1296.bu1', '1296.cc1', '1296.dy1', '1296.fg1'], 'contains': ['5184.b1', '7776.i1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [16057, 15552, 12384], 'label': '31104.fx.2592.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cu1', 'old_label': '2592.bt1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.bt1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247621
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.ea1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.cf1', '864.cj1', '864.cl1', '1296.bc1', '1296.bl1', '1296.bs1', '1296.bv1', '1296.cd1', '1296.dy2', '1296.fh1'], 'contains': ['5184.c1', '7776.i1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [2665, 18144, 12384], 'label': '31104.fx.2592.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ct1', 'old_label': '2592.bu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.bu1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247622
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ef1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.bz1', '864.cg1', '864.ch1', '1296.k1', '1296.bm1', '1296.ce1', '1296.cf1', '1296.cj1', '1296.ea1', '1296.es1'], 'contains': ['5184.d1', '7776.h1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [26029, 18144, 1728], 'label': '31104.fx.2592.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bc1', 'old_label': '2592.bv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.bv1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247623
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.ec1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.ca1', '864.ci1', '864.cj1', '1296.z1', '1296.bm1', '1296.by1', '1296.bz1', '1296.ce1', '1296.ec1', '1296.fe1'], 'contains': ['5184.d1', '7776.i1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [15625, 1728, 18144], 'label': '31104.fx.2592.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cp1', 'old_label': '2592.bw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.bw1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247624
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.fr1', '864.cb1', '864.ck1', '864.cm1', '1296.be1', '1296.ca1', '1296.et1'], 'contains': ['5184.f1', '7776.h1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [10909, 15552, 31084], 'label': '31104.fx.2592.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bj1', 'old_label': '2592.bx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.bx1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247625
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.bh1', '18.bj1', '18.bl1'], 'contains': ['108.el1', '108.em1', '108.fq1', '162.bh1', '162.bj1', '216.ma1'], 'core': '648.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1, 16056, 432, 22758, 10368, 15552, 2592, 28464], 'label': '31104.fx.54.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bx1', 'old_label': '54.bx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.bx1', 'subgroup_fusion': None, 'weyl_group': '576.5126'}
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id: 186247626
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.fs1', '864.cc1', '864.cl1', '864.cn1', '1296.be1', '1296.bw1', '1296.fi1'], 'contains': ['5184.f1', '7776.i1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [505, 15552, 18700], 'label': '31104.fx.2592.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.dz1', 'old_label': '2592.by1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.by1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247627
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.ft1', '864.cc1', '864.cl1', '864.co1', '1296.fl1'], 'contains': ['5184.g1', '7776.i1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [505, 15552, 29068], 'label': '31104.fx.2592.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1296.fl1', 'old_label': '2592.bz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.bz1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247628
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.fu1', '864.cd1', '864.cp1', '864.cq1', '1296.ew1'], 'contains': ['5184.h1', '7776.h1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [26029, 18144, 13852], 'label': '31104.fx.2592.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.bv1', 'old_label': '2592.ca1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.ca1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247629
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.cm1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.cr1', '864.cs1', '864.ct1', '1296.cn1', '1296.cs1', '1296.cv1', '1296.cw1', '1296.cx1', '1296.da1', '1296.dd1', '1296.di1', '1296.do1', '1296.dq1', '1296.dr1', '1296.ds1', '1296.dt1', '1296.ed1', '1296.fo1'], 'contains': ['5184.a1', '5184.j1', '7776.j1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [18144, 16056, 10368], 'label': '31104.fx.2592.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '2592.cb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.cb1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247630
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.cm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.ct1', '864.cu1', '864.cv1', '1296.co1', '1296.db1', '1296.de1', '1296.de2', '1296.dj1', '1296.dp1', '1296.du1', '1296.dv1', '1296.dw1', '1296.dx1', '1296.dy1', '1296.dy2', '1296.ee1', '1296.fp1', '1296.fq1'], 'contains': ['5184.b1', '5184.c1', '5184.k1', '7776.j1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [16056, 18144, 12384], 'label': '31104.fx.2592.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '2592.cc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.cc1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247631
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.cz1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.cr1', '864.cu1', '1296.cp1', '1296.ct1', '1296.cy1', '1296.dc1', '1296.df1', '1296.dk1', '1296.dn1', '1296.dz1', '1296.ea1', '1296.eb1', '1296.ec1', '1296.ef1', '1296.fr1'], 'contains': ['5184.d1', '5184.l1', '7776.j1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [18648, 18576, 12096], 'label': '31104.fx.2592.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '2592.cd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.cd1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247632
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.cs1', '864.cu1', '864.cv1', '1296.cq1', '1296.dg1', '1296.dg2', '1296.dl1', '1296.eh1', '1296.fr1', '1296.fs1'], 'contains': ['5184.d1', '5184.e1', '5184.n1', '7776.j1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [18144, 18648, 12096], 'label': '31104.fx.2592.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1', 'old_label': '2592.ce1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.ce1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247633
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.cr1', '864.cs1', '864.cv1', '1296.cr1', '1296.cu1', '1296.cz1', '1296.dh1', '1296.dm1', '1296.eg1', '1296.fs1'], 'contains': ['5184.e1', '5184.m1', '7776.j1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [15552, 2592, 12096], 'label': '31104.fx.2592.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.s1', 'old_label': '2592.cf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.cf1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247634
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.n1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.cw1', '864.cx1', '864.cy1', '864.cz1', '864.da1', '864.db1', '864.dc1', '864.dd1', '864.de1', '864.de2', '864.df1', '1296.el1', '1296.ep1', '1296.fa1', '1296.ff1', '1296.fo1'], 'contains': ['5184.a1', '7776.k1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [3096, 15552, 10368], 'label': '31104.fx.2592.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '2592.cg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.cg1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247635
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.df1', '864.dg1', '864.dj1', '864.dk1', '864.dm1', '864.do1', '864.dq1', '864.ds1', '864.du1', '1296.em1', '1296.eq1', '1296.fb1', '1296.fg1', '1296.fq1'], 'contains': ['5184.b1', '7776.k1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [3096, 15552, 12384], 'label': '31104.fx.2592.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '2592.ch1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.ch1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247636
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bj1', '18.bm1', '27.e1'], 'contains': ['108.bs1', '108.bt1', '108.ck1', '108.eo1', '108.fr1', '162.bh1'], 'core': '216.b1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [5713, 2592, 18576, 6, 72, 10368, 22752, 15552], 'label': '31104.fx.54.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '54.by1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.by1', 'subgroup_fusion': None, 'weyl_group': '576.7160'}
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id: 186247637
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.df1', '864.dh1', '864.di1', '864.dl1', '864.dn1', '864.dp1', '864.dr1', '864.dt1', '864.dv1', '1296.en1', '1296.er1', '1296.fc1', '1296.fh1', '1296.fp1'], 'contains': ['5184.c1', '7776.k1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [18216, 18144, 12384], 'label': '31104.fx.2592.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '2592.ci1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.ci1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247638
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.cw1', '864.dg1', '864.dh1', '1296.eo1', '1296.es1', '1296.fd1', '1296.fd2', '1296.fe1', '1296.fr1', '1296.fs1'], 'contains': ['5184.d1', '5184.e1', '7776.k1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [15552, 18648, 12096], 'label': '31104.fx.2592.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '2592.cj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.cj1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247639
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.bl1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.fx1', '864.cx1', '864.di1', '864.dj1', '864.dw1', '864.dx1', '864.ea1', '864.eb1', '1296.ei1', '1296.et1', '1296.fi1'], 'contains': ['5184.f1', '7776.k1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [3096, 15552, 24460], 'label': '31104.fx.2592.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1', 'old_label': '2592.ck1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.ck1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247640
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.bm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.cy1', '864.dk1', '864.dl1', '864.dy1', '864.dz1', '864.ea1', '864.eb1', '1296.ej1', '1296.eu1', '1296.ez1', '1296.fj1', '1296.ft1'], 'contains': ['7776.k1', '10368.d1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [6244, 72, 18144], 'label': '31104.fx.2592.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '2592.cl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.cl1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186247641
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.fy1', '864.cz1', '864.da1', '864.dm1', '864.dn1', '864.dw1', '864.dy1', '864.ea1', '864.ec1', '864.ed1', '1296.ek1', '1296.ev1', '1296.fk1'], 'contains': ['7776.k1', '10368.e1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [5712, 18648, 15552], 'label': '31104.fx.2592.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1', 'old_label': '2592.cm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.cm1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186247642
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.fz1', '864.cx1', '864.di1', '864.do1', '864.dy1', '864.dz1', '864.ec1', '864.ed1', '864.ee1', '864.ee2', '1296.fl1'], 'contains': ['5184.g1', '7776.k1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [3096, 15552, 10924], 'label': '31104.fx.2592.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.t1', 'old_label': '2592.cn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.cn1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247643
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.cy1', '864.dk1', '864.dp1', '864.dw1', '864.dx1', '864.ec1', '864.ed1', '864.ee1', '864.ee2', '1296.fm1', '1296.fu1'], 'contains': ['7776.k1', '10368.f1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [28996, 72, 18144], 'label': '31104.fx.2592.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '2592.co1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.co1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186247644
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.ga1', '864.cz1', '864.db1', '864.dm1', '864.dn1', '864.dw1', '864.dx1', '864.dy1', '864.dz1', '864.eb1', '864.ec1', '864.ee1', '864.ee2', '1296.fn1'], 'contains': ['7776.k1', '10368.g1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [28464, 18648, 15552], 'label': '31104.fx.2592.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.t1', 'old_label': '2592.cp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.cp1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186247645
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.gb1', '864.dc1', '864.dq1', '864.dr1', '1296.ew1'], 'contains': ['5184.h1', '5184.i1', '7776.k1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [18216, 18144, 11764], 'label': '31104.fx.2592.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.bv1', 'old_label': '2592.cq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.cq1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247646
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.df1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.dd1', '864.ds1', '864.dt1', '1296.ex1', '1296.fv1', '1296.fw1'], 'contains': ['7776.k1', '10368.h1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [29404, 18648, 15552], 'label': '31104.fx.2592.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cp1', 'old_label': '2592.cr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.cr1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186247647
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bi1', '27.a1'], 'contains': ['108.ep1', '108.fy1', '162.bi1', '864.ia1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [1, 16056, 18576, 6, 5712, 15552, 18144, 20812], 'label': '31104.fx.54.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.bz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.bz1', 'subgroup_fusion': None, 'weyl_group': '576.8654'}
-
id: 186247648
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.gc1', '864.de1', '864.de2', '864.du1', '864.dv1', '1296.ey1'], 'contains': ['7776.k1', '10368.i1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [29904, 18648, 15552], 'label': '31104.fx.2592.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.bx1', 'old_label': '2592.cs1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.cs1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186247649
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.i1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.ef1', '864.eg1', '864.eh1', '1296.a1', '1296.cn1', '1296.fx1', '1296.ga1', '1296.gb1', '1296.ge1', '1296.gf1', '1296.gg1', '1296.jw1', '1296.jw2'], 'contains': ['5184.j1', '5184.q1', '5184.bs1', '7776.l1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [36, 16056, 22752], 'label': '31104.fx.2592.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '2592.ct1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.ct1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247650
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.bd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.eh1', '864.ei1', '864.ej1', '1296.b1', '1296.c1', '1296.co1', '1296.gc1', '1296.gh1', '1296.jx1'], 'contains': ['5184.k1', '5184.r1', '5184.bt1', '7776.l1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [36, 16056, 12384], 'label': '31104.fx.2592.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.w1', 'old_label': '2592.cu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.cu1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247651
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.ef1', '864.ei1', '1296.d1', '1296.cp1', '1296.fy1', '1296.gd1', '1296.gi1', '1296.gk1', '1296.jy1'], 'contains': ['5184.l1', '5184.s1', '5184.bu3', '7776.l1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [36, 18576, 12096], 'label': '31104.fx.2592.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '2592.cv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.cv1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247652
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.ef1', '864.eg1', '864.ej1', '1296.e1', '1296.g1', '1296.cr1', '1296.fz1', '1296.gj1', '1296.jy1', '1296.jz1'], 'contains': ['5184.m1', '5184.s1', '5184.bu1', '7776.l1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [36, 16056, 12096], 'label': '31104.fx.2592.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.t1', 'old_label': '2592.cw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.cw1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247653
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.eg1', '864.ei1', '864.ej1', '1296.d1', '1296.f1', '1296.g1', '1296.cq1', '1296.jz1'], 'contains': ['5184.n1', '5184.s1', '5184.bu2', '7776.l1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [36, 432, 12096], 'label': '31104.fx.2592.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.di1', 'old_label': '2592.cx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.cx1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247654
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.kq1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.ek1', '864.en1', '1296.cs1', '1296.fx1', '1296.gl1', '1296.gm1', '1296.go1', '1296.gs1', '1296.gu1', '1296.gx1', '1296.hb1', '1296.hc1', '1296.hd1', '1296.hr1', '1296.hs1', '1296.ka1', '1296.kd1'], 'contains': ['5184.j1', '5184.t1', '7776.m1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [12138, 16056, 22752], 'label': '31104.fx.2592.cy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '2592.cy1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.cy1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247655
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.le1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.ek1', '864.el1', '1296.ct1', '1296.fy1', '1296.gn1', '1296.gp1', '1296.gr1', '1296.gt1', '1296.gv1', '1296.gy1', '1296.ha1', '1296.he1', '1296.hf1', '1296.hg1', '1296.hh1', '1296.kb1', '1296.ke1'], 'contains': ['5184.l1', '5184.u1', '7776.m1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [17371, 18576, 12096], 'label': '31104.fx.2592.cz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '2592.cz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.cz1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247656
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.me1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.ek1', '864.em1', '1296.cu1', '1296.fz1', '1296.gq1', '1296.gw1', '1296.gz1', '1296.kc1', '1296.ke1'], 'contains': ['5184.m1', '5184.u1', '7776.m1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [17371, 2592, 12096], 'label': '31104.fx.2592.da1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.j1', 'old_label': '2592.da1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.da1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247657
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.kz1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.el1', '864.em1', '864.en1', '1296.cv1', '1296.ga1', '1296.hi1', '1296.hj1', '1296.hk1', '1296.hl1', '1296.hm1', '1296.hn1', '1296.ho1', '1296.hp1', '1296.hq1', '1296.hr1', '1296.hs1', '1296.kh1', '1296.kj1'], 'contains': ['5184.j1', '5184.x1', '7776.m1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [17371, 18576, 22752], 'label': '31104.fx.2592.db1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '2592.db1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.db1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247658
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bh1'], 'contains': ['108.eq1', '108.fz1', '162.bj1', '864.ib1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1, 16056, 18576, 22758, 28464, 15552, 18144, 76], 'label': '31104.fx.54.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.ca1', 'old_label': '54.ca1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.ca1', 'subgroup_fusion': None, 'weyl_group': '576.8654'}
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id: 186247659
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.iu1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.eo1', '864.ep1', '864.eq1', '1296.cw1', '1296.ga1', '1296.gl1', '1296.gm1', '1296.hi1', '1296.ht1', '1296.hu1', '1296.hv1', '1296.hw1', '1296.hx1', '1296.hy1', '1296.in1', '1296.io1', '1296.kk1', '1296.kl1'], 'contains': ['5184.j1', '5184.z1', '7776.n1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [6, 16056, 10368], 'label': '31104.fx.2592.dc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '2592.dc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.dc1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247660
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.jr1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.eq1', '864.er1', '1296.cx1', '1296.fx1', '1296.go1', '1296.hj1', '1296.hk1', '1296.hz1', '1296.ib1', '1296.ie1', '1296.ii1', '1296.ij1', '1296.ik1', '1296.in1', '1296.io1', '1296.ko1', '1296.ku1'], 'contains': ['5184.j1', '5184.bc1', '7776.n1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [6, 16056, 22752], 'label': '31104.fx.2592.dd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '2592.dd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.dd1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247661
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.jt1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.eo1', '864.er1', '1296.cy1', '1296.fy1', '1296.gn1', '1296.gp1', '1296.gr1', '1296.ia1', '1296.ic1', '1296.if1', '1296.ih1', '1296.il1', '1296.im1', '1296.ip1', '1296.iq1', '1296.kp1', '1296.kv1'], 'contains': ['5184.l1', '5184.bd1', '7776.n1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26047, 18576, 12096], 'label': '31104.fx.2592.de1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '2592.de1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.de1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247662
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.kj1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.ep1', '864.er1', '1296.cz1', '1296.fz1', '1296.gq1', '1296.id1', '1296.ig1', '1296.kq1', '1296.kv1'], 'contains': ['5184.m1', '5184.bd1', '7776.n1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [26047, 2592, 12096], 'label': '31104.fx.2592.df1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.k1', 'old_label': '2592.df1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.df1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247663
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.es1', '864.et1', '1296.da1', '1296.gb1', '1296.gl1', '1296.gs1', '1296.hj1', '1296.hl1', '1296.ht1', '1296.hz1', '1296.ir1', '1296.it1', '1296.it2', '1296.iv1', '1296.iw1', '1296.kw1', '1296.kw2'], 'contains': ['5184.j1', '5184.bh1', '7776.o1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [10405, 2592, 22752], 'label': '31104.fx.2592.dg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '2592.dg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.dg1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247664
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.di1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.es1', '864.eu1', '1296.db1', '1296.gc1', '1296.is1', '1296.iu1', '1296.kx1'], 'contains': ['5184.k1', '5184.bi1', '7776.o1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [10405, 2592, 12384], 'label': '31104.fx.2592.dh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.n1', 'old_label': '2592.dh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.dh1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247665
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.et1', '864.eu1', '1296.dc1', '1296.gd1', '1296.gn1', '1296.gt1', '1296.ia1', '1296.ix1', '1296.iy1', '1296.iz1', '1296.ky1'], 'contains': ['5184.l1', '5184.bj1', '7776.o1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [10405, 2592, 1728], 'label': '31104.fx.2592.di1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '2592.di1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.di1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247666
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.ev1', '864.ew1', '864.ew2', '864.ex1', '1296.a1', '1296.l1', '1296.s1', '1296.dd1', '1296.lb1', '1296.lb2'], 'contains': ['5184.j1', '5184.bp1', '5184.bs1', '7776.p1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [15588, 16056, 10368], 'label': '31104.fx.2592.dj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.dg1', 'old_label': '2592.dj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.dj1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 186247667
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.ex1', '864.ey1', '864.ez1', '864.ez2', '1296.b1', '1296.n1', '1296.t1', '1296.de2', '1296.lc1'], 'contains': ['5184.k1', '5184.bq2', '5184.bt1', '7776.p1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [15588, 16056, 12384], 'label': '31104.fx.2592.dk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.dh1', 'old_label': '2592.dk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.dk1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247668
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.dk2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.ex1', '864.ey2', '864.ez3', '1296.c1', '1296.m1', '1296.u1', '1296.de1', '1296.lc1'], 'contains': ['5184.k1', '5184.bq1', '5184.bt1', '7776.p1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [3060, 16056, 12384], 'label': '31104.fx.2592.dk2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.dh1', 'old_label': '2592.dk2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.dk2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247669
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '9.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3.b1'], 'contains': ['18.k1', '18.m1', '18.q1', '18.u1', '18.bb1', '18.be1', '18.bk1', '27.c1', '27.d1', '36.di1'], 'core': '108.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [5713, 2592, 12096, 22752, 15552, 6, 5260, 18576, 2664, 36], 'label': '31104.fx.9.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '9.b1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.b1', 'subgroup_fusion': None, 'weyl_group': '3456.gu'}
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id: 186247670
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.bh1', '18.bi1'], 'contains': ['108.er1', '108.es1', '108.ga1', '162.bi1', '162.bj1', '864.ic1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1, 16056, 18576, 22758, 28464, 15552, 18144, 20812], 'label': '31104.fx.54.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.cb1', 'old_label': '54.cb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.cb1', 'subgroup_fusion': None, 'weyl_group': '576.8654'}
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id: 186247671
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.ev1', '864.ey1', '864.ey2', '1296.d1', '1296.o1', '1296.v1', '1296.df1', '1296.ld1'], 'contains': ['5184.l1', '5184.br2', '5184.bu2', '7776.p1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [15588, 18576, 12096], 'label': '31104.fx.2592.dl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.di1', 'old_label': '2592.dl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.dl1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247672
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.ev1', '864.ew1', '864.ez2', '864.ez3', '1296.e1', '1296.p2', '1296.r1', '1296.y1', '1296.dh1', '1296.ld2', '1296.le1'], 'contains': ['5184.m1', '5184.br1', '5184.bu1', '7776.p1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [18684, 2592, 12096], 'label': '31104.fx.2592.dm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.di1', 'old_label': '2592.dm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.dm1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247673
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.dm2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.ev1', '864.ew2', '864.ez1', '864.ez3', '1296.g1', '1296.p1', '1296.r2', '1296.w1', '1296.dh1', '1296.ld1', '1296.le1'], 'contains': ['5184.m1', '5184.br2', '5184.bu2', '7776.p1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [3132, 2592, 12096], 'label': '31104.fx.2592.dm2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.di1', 'old_label': '2592.dm2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.dm2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247674
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.ew1', '864.ew2', '864.ey1', '864.ez3', '1296.g1', '1296.o1', '1296.q1', '1296.y1', '1296.dg2', '1296.le1', '1296.le2'], 'contains': ['5184.n1', '5184.br2', '5184.bu1', '7776.p1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [2700, 432, 12096], 'label': '31104.fx.2592.dn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.di1', 'old_label': '2592.dn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.dn1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247675
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.dn2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.ew1', '864.ey2', '864.ez1', '1296.d1', '1296.r2', '1296.x1', '1296.dg1', '1296.le2'], 'contains': ['5184.n1', '5184.br2', '5184.bu3', '7776.p1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [18612, 432, 12096], 'label': '31104.fx.2592.dn2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.di1', 'old_label': '2592.dn2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.dn2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247676
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.dn3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.ew2', '864.ey2', '864.ez2', '1296.f1', '1296.r1', '1296.v1', '1296.dg1', '1296.le1'], 'contains': ['5184.n1', '5184.br1', '5184.bu2', '7776.p1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [108, 432, 12096], 'label': '31104.fx.2592.dn3', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.di1', 'old_label': '2592.dn3', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.dn3', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247677
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.bd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.fa1', '864.fb1', '864.fc1', '1296.s1', '1296.cn1', '1296.gu1', '1296.hm1', '1296.hu1', '1296.ib1', '1296.ir1', '1296.ja1', '1296.lb1', '1296.lb2'], 'contains': ['5184.j1', '5184.bp1', '7776.q1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [18180, 16056, 22752], 'label': '31104.fx.2592.do1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '2592.do1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.do1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247678
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.bd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.fc1', '864.fd1', '864.fe1', '1296.t1', '1296.u1', '1296.co1', '1296.is1', '1296.jb1', '1296.lc1'], 'contains': ['5184.k1', '5184.bq1', '5184.bq2', '7776.q1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [18180, 16056, 12384], 'label': '31104.fx.2592.dp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.w1', 'old_label': '2592.dp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.dp1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247679
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.fa1', '864.fd1', '1296.v1', '1296.cp1', '1296.gv1', '1296.ic1', '1296.ix1', '1296.jc1', '1296.ld2'], 'contains': ['5184.l1', '5184.br1', '7776.q1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [108, 18576, 12096], 'label': '31104.fx.2592.dq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '2592.dq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.dq1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247680
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.fa1', '864.fb1', '864.fe1', '1296.w1', '1296.y1', '1296.cr1', '1296.gw1', '1296.id1', '1296.ld1', '1296.le2'], 'contains': ['5184.m1', '5184.br2', '7776.q1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [18180, 16056, 12096], 'label': '31104.fx.2592.dr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.t1', 'old_label': '2592.dr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.dr1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247681
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bh1'], 'contains': ['108.et1', '108.gc2', '162.bj1', '864.id1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1, 16056, 18576, 14406, 19248, 15552, 18144, 76], 'label': '31104.fx.54.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.cc1', 'old_label': '54.cc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.cc1', 'subgroup_fusion': None, 'weyl_group': '576.8654'}
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id: 186247682
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.fb1', '864.fd1', '864.fe1', '1296.v1', '1296.x1', '1296.y1', '1296.cq1', '1296.le1'], 'contains': ['5184.n1', '5184.br1', '5184.br2', '7776.q1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [18684, 432, 12096], 'label': '31104.fx.2592.ds1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.di1', 'old_label': '2592.ds1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.ds1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247683
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.bc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.ff1', '864.fg2', '864.fh1', '1296.l1', '1296.di1', '1296.gx1', '1296.hi1', '1296.ie1', '1296.it2', '1296.je2', '1296.jh1', '1296.jw1', '1296.lb2'], 'contains': ['5184.j1', '5184.bs1', '7776.r1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [468, 16056, 22752], 'label': '31104.fx.2592.dt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '2592.dt1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.dt1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247684
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.dt2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.ff2', '864.fg1', '864.fh1', '1296.l1', '1296.di1', '1296.go1', '1296.hn1', '1296.hv1', '1296.it1', '1296.je1', '1296.jg1', '1296.jw2', '1296.lb1'], 'contains': ['5184.j1', '5184.bs1', '7776.r1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [468, 16056, 10368], 'label': '31104.fx.2592.dt2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '2592.dt2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.dt2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247685
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.fh1', '864.fi1', '864.fj1', '1296.m1', '1296.n1', '1296.dj1', '1296.iu1', '1296.jf1', '1296.jx1', '1296.lc1'], 'contains': ['5184.k1', '5184.bt1', '7776.r1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [468, 16056, 12384], 'label': '31104.fx.2592.du1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.w1', 'old_label': '2592.du1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.du1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 186247686
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.dv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.ff1', '864.ff2', '864.fi1', '1296.o1', '1296.dk1', '1296.gp1', '1296.gy1', '1296.if1', '1296.iy1', '1296.jd1', '1296.ji1', '1296.jy1', '1296.ld2'], 'contains': ['5184.l1', '5184.bu1', '7776.r1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [2628, 18576, 12096], 'label': '31104.fx.2592.dv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '2592.dv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.dv1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247687
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.ff1', '864.fg1', '864.fj1', '1296.p1', '1296.r1', '1296.dm1', '1296.gz1', '1296.ig1', '1296.jz1', '1296.ld1'], 'contains': ['5184.m1', '5184.bu2', '7776.r1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [3060, 2592, 12096], 'label': '31104.fx.2592.dw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.t1', 'old_label': '2592.dw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.dw1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247688
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.dw2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.ff2', '864.fg2', '864.fj1', '1296.p2', '1296.r2', '1296.dm1', '1296.gq1', '1296.jj1', '1296.jy1', '1296.le2'], 'contains': ['5184.m1', '5184.bu1', '5184.bu3', '7776.r1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [18612, 2592, 12096], 'label': '31104.fx.2592.dw2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.t1', 'old_label': '2592.dw2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.dw2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247689
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.dx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.fg1', '864.fg2', '864.fi1', '864.fj1', '1296.o1', '1296.q1', '1296.r1', '1296.r2', '1296.dl1', '1296.jz1', '1296.le1'], 'contains': ['5184.n1', '5184.bu1', '5184.bu2', '7776.r1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [2628, 432, 12096], 'label': '31104.fx.2592.dx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.di1', 'old_label': '2592.dx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.dx1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247690
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.fk1', '864.fl1', '1296.dn1', '1296.gd1', '1296.ha1', '1296.hg1', '1296.ih1', '1296.ip1', '1296.ix1', '1296.jd1', '1296.jk1', '1296.jl1', '1296.lf1'], 'contains': ['5184.l1', '5184.bv1', '7776.s1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1, 2592, 1728], 'label': '31104.fx.2592.dy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '2592.dy1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.dy1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247691
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.z1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.fk1', '864.fm1', '1296.do1', '1296.gb1', '1296.hb1', '1296.ho1', '1296.hr1', '1296.hw1', '1296.ii1', '1296.in1', '1296.ir1', '1296.je1', '1296.je2', '1296.jm1', '1296.jn1', '1296.lg1', '1296.lg2'], 'contains': ['5184.j1', '5184.bw1', '7776.s1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1, 2592, 22752], 'label': '31104.fx.2592.dz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '2592.dz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.dz1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247692
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.bh1', '18.bi1', '18.bj1', '27.b1'], 'contains': ['108.eh1', '108.ev1', '108.fo1', '162.bh1', '162.bi1', '162.bj1', '216.mc1'], 'core': '648.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [5713, 2664, 18576, 6, 10368, 15552, 2592, 15628], 'label': '31104.fx.54.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '54.cd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.cd1', 'subgroup_fusion': None, 'weyl_group': '1152.155790'}
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id: 186247693
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.dc1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.fl1', '864.fm1', '1296.dp1', '1296.gc1', '1296.is1', '1296.jf1', '1296.lh1'], 'contains': ['5184.k1', '5184.bx1', '7776.s1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1, 2592, 12384], 'label': '31104.fx.2592.ea1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.p1', 'old_label': '2592.ea1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.ea1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247694
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.eb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.lr1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.fn1', '864.fv1', '1296.cs1', '1296.ge1', '1296.ho1', '1296.hp1', '1296.ht1', '1296.hx1', '1296.ib1', '1296.ie1', '1296.iv1', '1296.jg1', '1296.jm1', '1296.jo1', '1296.jq1', '1296.ka1', '1296.lk1'], 'contains': ['5184.j1', '7776.t1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [30282, 22752, 16056], 'label': '31104.fx.2592.eb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '2592.eb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.eb1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247695
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.ec1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.lb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.fo1', '864.fp1', '864.fv1', '1296.cv1', '1296.gf1', '1296.hb1', '1296.hc1', '1296.hu1', '1296.hv1', '1296.hz1', '1296.ij1', '1296.iw1', '1296.jh1', '1296.jm1', '1296.jp1', '1296.jq1', '1296.kh1', '1296.ll1'], 'contains': ['5184.j1', '7776.t1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [2179, 18576, 22752], 'label': '31104.fx.2592.ec1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '2592.ec1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.ec1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247696
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.ed1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bf1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.fq1', '864.fw1', '1296.dq1', '1296.gg1', '1296.gm1', '1296.hd1', '1296.hk1', '1296.hq1', '1296.hx1', '1296.ij1', '1296.ja1', '1296.je1', '1296.je2', '1296.jo1', '1296.jp1', '1296.kw1', '1296.kw2'], 'contains': ['5184.j1', '7776.u1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26389, 22752, 2592], 'label': '31104.fx.2592.ed1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '2592.ed1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.ed1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247697
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.ee1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.iz1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.fr1', '864.fs1', '864.fx1', '1296.cw1', '1296.gf1', '1296.gs1', '1296.hd1', '1296.hm1', '1296.hn1', '1296.ii1', '1296.ik1', '1296.iv1', '1296.jh1', '1296.jn1', '1296.jo1', '1296.jr1', '1296.kk1', '1296.lm1'], 'contains': ['5184.j1', '7776.v1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [18150, 10368, 16056], 'label': '31104.fx.2592.ee1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '2592.ee1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.ee1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247698
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.ef1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.jx1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.ft1', '864.fx1', '1296.cx1', '1296.ge1', '1296.gu1', '1296.gx1', '1296.hl1', '1296.hq1', '1296.hw1', '1296.hy1', '1296.iw1', '1296.jg1', '1296.jn1', '1296.jp1', '1296.jr1', '1296.ko1', '1296.ln1'], 'contains': ['5184.j1', '7776.v1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [18150, 16056, 22752], 'label': '31104.fx.2592.ef1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '2592.ef1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.ef1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247699
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.eg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.bd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.fu1', '864.fy1', '1296.ds1', '1296.gg1', '1296.hc1', '1296.hp1', '1296.hs1', '1296.hy1', '1296.ik1', '1296.io1', '1296.it1', '1296.it2', '1296.ja1', '1296.jq1', '1296.jr1', '1296.lg1', '1296.lg2'], 'contains': ['5184.j1', '7776.w1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [15985, 2592, 22752], 'label': '31104.fx.2592.eg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '2592.eg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.eg1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247700
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.eh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ec1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.fw1', '864.fz1', '1296.du1', '1296.gh1', '1296.jb1', '1296.jf1', '1296.kx1'], 'contains': ['5184.k1', '7776.u1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [28981, 12384, 2592], 'label': '31104.fx.2592.eh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.n1', 'old_label': '2592.eh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.eh1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247701
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.ei1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.dz1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.fy1', '864.ga1', '1296.dx1', '1296.gh1', '1296.iu1', '1296.jb1', '1296.lh1'], 'contains': ['5184.k1', '7776.w1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [18577, 2592, 12384], 'label': '31104.fx.2592.ei1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.p1', 'old_label': '2592.ei1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.ei1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247702
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.lc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.fn1', '864.fo1', '1296.ct1', '1296.gi1', '1296.ha1', '1296.he1', '1296.ia1', '1296.ic1', '1296.if1', '1296.il1', '1296.iz1', '1296.ji1', '1296.jk1', '1296.js1', '1296.jt1', '1296.kb1', '1296.lo1'], 'contains': ['5184.l1', '7776.t1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [19891, 12096, 18576], 'label': '31104.fx.2592.ej1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '2592.ej1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.ej1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 186247703
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '54.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.bk1', '18.bl1', '18.bm1', '27.d1'], 'contains': ['108.bq1', '108.bw1', '108.bx1', '108.ci1', '108.ei1', '108.eu1', '108.fl1', '162.bh1', '162.bk1'], 'core': '648.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [5713, 2592, 18576, 6, 72, 22752, 12096, 15552], 'label': '31104.fx.54.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '54.ce1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.ce1', 'subgroup_fusion': None, 'weyl_group': '576.7160'}
-
id: 186247704
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ob1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.fn1', '864.fp1', '1296.cu1', '1296.gj1', '1296.id1', '1296.ig1', '1296.jj1', '1296.kc1', '1296.lp1'], 'contains': ['5184.m1', '7776.t1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1819, 12096, 2592], 'label': '31104.fx.2592.ek1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.j1', 'old_label': '2592.ek1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.ek1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247705
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.el1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bl1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.fq1', '864.fz1', '1296.dz1', '1296.gk1', '1296.gr1', '1296.hf1', '1296.il1', '1296.jc1', '1296.jd1', '1296.js1', '1296.ky1'], 'contains': ['5184.l1', '7776.u1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [26389, 2592, 1728], 'label': '31104.fx.2592.el1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '2592.el1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.el1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247706
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.em1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.jc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.fr1', '864.ft1', '1296.cy1', '1296.gi1', '1296.gt1', '1296.gv1', '1296.gy1', '1296.hf1', '1296.ih1', '1296.im1', '1296.iz1', '1296.ji1', '1296.jl1', '1296.js1', '1296.ju1', '1296.kp1', '1296.lq2'], 'contains': ['5184.l1', '7776.v1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [2598, 18576, 12096], 'label': '31104.fx.2592.em1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '2592.em1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.em1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247707
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.en1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.ll1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.fs1', '864.ft1', '1296.cz1', '1296.gj1', '1296.gw1', '1296.gz1', '1296.jj1', '1296.kq1', '1296.lq1'], 'contains': ['5184.m1', '7776.v1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [10495, 2592, 12096], 'label': '31104.fx.2592.en1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.k1', 'old_label': '2592.en1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.en1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247708
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.eo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.bf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.fu1', '864.ga1', '1296.eb1', '1296.gk1', '1296.he1', '1296.hh1', '1296.im1', '1296.iq1', '1296.iy1', '1296.jc1', '1296.jt1', '1296.ju1', '1296.lf1'], 'contains': ['5184.l1', '7776.w1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [15985, 1728, 2592], 'label': '31104.fx.2592.eo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '2592.eo1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.eo1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247709
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.ep1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.cj1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.gb1', '864.ge1', '864.gh3', '864.gi1', '1296.ed1', '1296.jw1', '1296.ka1', '1296.kj1', '1296.kl1', '1296.ko1', '1296.kw1', '1296.lb1', '1296.lg1', '1296.ll1', '1296.lm1'], 'contains': ['5184.j1', '7776.x1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [16056, 18576, 10368], 'label': '31104.fx.2592.ep1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '2592.ep1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.ep1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247710
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.ep2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.bs1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.gc1', '864.gd1', '864.gf1', '864.gg1', '864.gh1', '864.gh2', '864.gi1', '1296.ed1', '1296.jw2', '1296.kd1', '1296.kh1', '1296.kk1', '1296.ku1', '1296.kw2', '1296.lb2', '1296.lg2', '1296.lk1', '1296.ln1'], 'contains': ['5184.j1', '7776.x1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [16056, 18576, 22752], 'label': '31104.fx.2592.ep2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '648.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '2592.ep2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.ep2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247711
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.eq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.gi1', '864.gj1', '864.gk1', '864.gl1', '1296.ee1', '1296.jx1', '1296.kx1', '1296.lc1', '1296.lh1'], 'contains': ['5184.k1', '7776.x1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [16056, 18576, 24768], 'label': '31104.fx.2592.eq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1', 'old_label': '2592.eq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.eq1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247712
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.er1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.bs1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.gb1', '864.gc1', '864.gj1', '1296.ef1', '1296.eg1', '1296.jy1', '1296.kb1', '1296.ke1', '1296.kp1', '1296.kv1', '1296.ky1', '1296.ld1', '1296.ld2', '1296.lf1', '1296.lo1', '1296.lp1', '1296.lq1', '1296.lq2'], 'contains': ['5184.l1', '5184.m1', '7776.x1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [2592, 18576, 12096], 'label': '31104.fx.2592.er1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '2592.er1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.er1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247713
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.es1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.gb1', '864.gd1', '864.gj1', '1296.eg1', '1296.eh1', '1296.jz1', '1296.kc1', '1296.kq1', '1296.le1', '1296.le2'], 'contains': ['5184.m1', '5184.n1', '7776.x1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [504, 15984, 12096], 'label': '31104.fx.2592.es1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.s1', 'old_label': '2592.es1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.es1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247714
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '64.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '32.b1', '32.c1'], 'contains': ['128.a1', '192.b1', '192.c1', '192.d1'], 'core': '576.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [36, 10368, 12384, 18580, 5712, 12096], 'label': '31104.fx.64.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.d1', 'old_label': '64.a1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.a1', 'subgroup_fusion': None, 'weyl_group': '1944.2342'}
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id: 186247715
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.et1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ha1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.fy1', '864.ge1', '864.gf1', '864.gk1', '1296.jv1', '1296.kf1', '1296.ki1', '1296.km1', '1296.kr1', '1296.kz1', '1296.li1'], 'contains': ['7776.x1', '10368.e1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [20812, 2664, 18576], 'label': '31104.fx.2592.et1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.dj1', 'old_label': '2592.et1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.et1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186247716
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.eu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.bu1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.ga1', '864.ge1', '864.gg1', '864.gk1', '1296.kn1', '1296.ks1', '1296.lj1'], 'contains': ['7776.x1', '10368.g1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [76, 2664, 18576], 'label': '31104.fx.2592.eu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.fb1', 'old_label': '2592.eu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.eu1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186247717
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.ev1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.bj1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.gc1', '864.gh1', '864.gh3', '864.gl1', '1296.kg1', '1296.kt1', '1296.la1'], 'contains': ['7776.x1', '10368.i1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [29904, 15984, 2592], 'label': '31104.fx.2592.ev1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.es1', 'old_label': '2592.ev1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.ev1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186247718
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.ev2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.gc1', '864.gh2', '864.gh3', '864.gl1', '1296.kt2'], 'contains': ['7776.x1', '10368.i1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [6556, 2664, 18576], 'label': '31104.fx.2592.ev2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fi1', 'old_label': '2592.ev2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.ev2', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186247719
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.ew1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ew1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.id1', '864.gm1', '864.go1', '864.gp1', '1296.lr1'], 'contains': ['5184.p1', '5184.v1', '5184.ba1', '7776.y1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 2592, 'diagramx': None, 'generators': [19135, 36, 16080], 'label': '31104.fx.2592.ew1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1296.lr1', 'old_label': '2592.ew1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.ew1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247720
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.ex1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ex1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.ie1', '864.gm1', '864.gq1', '864.gr1', '1296.lr1'], 'contains': ['5184.p1', '5184.y1', '5184.be1', '7776.y1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [24198, 36, 16080], 'label': '31104.fx.2592.ex1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.oi1', 'old_label': '2592.ex1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.ex1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247721
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.ey1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.ea1', '864.gn1', '864.gs1', '864.gv1', '864.gw1', '1296.bd1'], 'contains': ['5184.o1', '5184.bk1', '5184.by1', '7776.z1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [20737, 36, 12940], 'label': '31104.fx.2592.ey1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1296.bd1', 'old_label': '2592.ey1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.ey1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247722
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.ez1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.eb1', '648.if1', '864.gn1', '864.gt1', '864.gu1', '864.gx1', '1296.lr1'], 'contains': ['5184.p1', '5184.bl1', '5184.bz1', '7776.z1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 2592, 'diagramx': None, 'generators': [20737, 36, 12460], 'label': '31104.fx.2592.ez1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1296.lr1', 'old_label': '2592.ez1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.ez1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247723
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.fa1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.jf1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.go1', '864.gq1', '864.gy1', '864.ha1', '1296.fx1', '1296.lt1'], 'contains': ['5184.q1', '5184.t1', '5184.bc1', '7776.y1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [29503, 36, 10368], 'label': '31104.fx.2592.fa1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ge1', 'old_label': '2592.fa1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.fa1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247724
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.fb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cr1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.gy1', '864.gz1', '1296.fy1', '1296.fz1', '1296.ls1'], 'contains': ['5184.s1', '5184.u1', '5184.bd1', '7776.y1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [26047, 36, 12096], 'label': '31104.fx.2592.fb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.ep1', 'old_label': '2592.fb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.fb1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247725
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '64.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.b1', '32.b1', '32.d1', '32.e1'], 'contains': ['128.a1', '192.e1', '192.f1', '192.g1', '192.h1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [17371, 22752, 23836, 8304, 12096, 10368], 'label': '31104.fx.64.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.d1', 'old_label': '64.b1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.b1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
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id: 186247726
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.fc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.jk1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.gp1', '864.gr1', '864.gz1', '864.ha1', '1296.ga1', '1296.lt1'], 'contains': ['5184.q1', '5184.x1', '5184.z1', '7776.y1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [19135, 36, 22752], 'label': '31104.fx.2592.fc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.gd1', 'old_label': '2592.fc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.fc1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247727
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.fd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.gs1', '864.gt1', '864.gu1', '864.hb1', '864.hc1', '1296.bf1', '1296.gb1', '1296.lt1'], 'contains': ['5184.q1', '5184.bh1', '5184.bw1', '7776.z1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [1, 36, 10368], 'label': '31104.fx.2592.fd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.c1', 'old_label': '2592.fd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.fd1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247728
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.fe1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.gv1', '864.gw1', '864.gx1', '864.hb1', '864.hd1', '1296.bg1', '1296.bh1', '1296.gc1'], 'contains': ['5184.r1', '5184.bi1', '5184.bx1', '7776.z1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [20737, 36, 12384], 'label': '31104.fx.2592.fe1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.o1', 'old_label': '2592.fe1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.fe1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247729
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.ff1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.hc1', '864.hd1', '1296.bi1', '1296.gd1', '1296.ls1'], 'contains': ['5184.s1', '5184.bj1', '5184.bv1', '7776.z1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [20737, 36, 1728], 'label': '31104.fx.2592.ff1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.a1', 'old_label': '2592.ff1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.ff1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247730
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.fg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.gl1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.he1', '864.hf1', '864.hg1', '864.hi1', '864.hj1', '1296.gl1', '1296.lt1', '1296.lv1'], 'contains': ['5184.t1', '5184.z1', '5184.bh1', '7776.ba1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [26485, 12138, 22752], 'label': '31104.fx.2592.fg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.gl1', 'old_label': '2592.fg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.fg1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247731
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.fh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.hr1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.he1', '864.hn1', '1296.gn1', '1296.ls1', '1296.lu1'], 'contains': ['5184.u1', '5184.bd1', '5184.bj1', '7776.ba1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [26485, 6, 12096], 'label': '31104.fx.2592.fh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.hw1', 'old_label': '2592.fh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.fh1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247732
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.fi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.fa1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.jf1', '864.hf1', '864.hk1', '864.ho1', '1296.lr1'], 'contains': ['5184.v1', '5184.be1', '5184.bl1', '7776.ba1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [26485, 30714, 28012], 'label': '31104.fx.2592.fi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.ok1', 'old_label': '2592.fi1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.fi1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247733
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.fj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.jg1', '864.hg1', '864.hp1'], 'contains': ['5184.w1', '5184.bg1', '5184.bn1', '7776.ba1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 1728, 'diagramx': None, 'generators': [13861, 6, 19536], 'label': '31104.fx.2592.fj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '864.hg1', 'old_label': '2592.fj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.fj1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247734
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.fk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cp1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.hh1', '864.hm1', '1296.fx1', '1296.go1', '1296.lv1'], 'contains': ['5184.t1', '5184.bc1', '5184.bs1', '7776.bb1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [29503, 18612, 10368], 'label': '31104.fx.2592.fk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.eq1', 'old_label': '2592.fk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.fk1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247735
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.fl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cr1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.hh1', '864.hl1', '1296.fy1', '1296.gq1', '1296.lu1'], 'contains': ['5184.u1', '5184.bd1', '5184.bu3', '7776.bb1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [26047, 18612, 12096], 'label': '31104.fx.2592.fl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.ep1', 'old_label': '2592.fl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.fl1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247736
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '64.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.c1', '32.b1', '32.d1', '32.f1'], 'contains': ['128.a1', '192.i1', '192.j1', '192.k1', '192.l1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [26047, 22752, 10368, 8304, 3100, 12096], 'label': '31104.fx.64.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.d1', 'old_label': '64.c1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.c1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
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id: 186247737
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.fl2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.co1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.hh1', '864.hl2', '1296.fz1', '1296.gp1', '1296.gq1'], 'contains': ['5184.u1', '5184.bd1', '5184.bu1', '7776.bb1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [6, 16092, 12096], 'label': '31104.fx.2592.fl2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.ik1', 'old_label': '2592.fl2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.fl2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247738
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.fm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.hg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.hq1', '1296.hg1', '1296.ls1', '1296.lu1'], 'contains': ['5184.u1', '5184.bv1', '7776.bc1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [5713, 12138, 12096], 'label': '31104.fx.2592.fm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.gh1', 'old_label': '2592.fm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.fm1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247739
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.fn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.fc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.jk1', '864.hi1', '864.hk1', '864.hv1', '1296.lr1'], 'contains': ['5184.y1', '5184.ba1', '5184.bl1', '7776.ba1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [7477, 18582, 5260], 'label': '31104.fx.2592.fn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.oj1', 'old_label': '2592.fn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.fn1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247740
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.fo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cm1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.hl1', '864.hl2', '864.hm1', '1296.ga1', '1296.hi1', '1296.lv1'], 'contains': ['5184.x1', '5184.z1', '5184.bs1', '7776.bb1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [19135, 18612, 22752], 'label': '31104.fx.2592.fo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.er1', 'old_label': '2592.fo1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.fo1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247741
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.fp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.hj1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.hj1', '864.hn1', '864.ho1', '864.hp1', '864.hv1', '1296.hj1', '1296.lt1', '1296.lv1'], 'contains': ['5184.x1', '5184.bc1', '5184.bh1', '7776.ba1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [26485, 12138, 10368], 'label': '31104.fx.2592.fp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.hy1', 'old_label': '2592.fp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.fp1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247742
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.fq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.gn1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.hq1', '864.hr1', '864.hs1', '864.hw1', '1296.hr1', '1296.lt1', '1296.lv1'], 'contains': ['5184.t1', '5184.x1', '5184.bw1', '7776.bc1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [5713, 12138, 10368], 'label': '31104.fx.2592.fq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.hw1', 'old_label': '2592.fq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.fq1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 186247743
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.fr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.jq1', '864.hr1', '864.ht1', '864.hu1', '864.hw1', '1296.lr1'], 'contains': ['5184.v1', '5184.y1', '5184.bz1', '7776.bc1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 2592, 'diagramx': None, 'generators': [1, 12138, 5712], 'label': '31104.fx.2592.fr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1296.lr1', 'old_label': '2592.fr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.fr1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247744
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.fs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bi1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.hx1', '864.hy1', '864.hz1', '864.ie1', '864.if1', '1296.in1', '1296.lt1', '1296.lv1'], 'contains': ['5184.z1', '5184.bc1', '5184.bw1', '7776.bd1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [5713, 6, 22752], 'label': '31104.fx.2592.fs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.gl1', 'old_label': '2592.fs1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.fs1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247745
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.ft1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.kc1', '864.hx1', '864.ia1', '864.ic1', '864.ie1', '1296.lr1'], 'contains': ['5184.ba1', '5184.be1', '5184.bz1', '7776.bd1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 2592, 'diagramx': None, 'generators': [1, 6, 5712], 'label': '31104.fx.2592.ft1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1296.lr1', 'old_label': '2592.ft1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.ft1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247746
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.fu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.kd1', '864.hy1', '864.ib1', '864.ic1', '864.id1', '864.ie1'], 'contains': ['5184.bb1', '5184.bf1', '5184.cb1', '7776.bd1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 5184, 'diagramx': None, 'generators': [5713, 18582, 15628], 'label': '31104.fx.2592.fu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2592.fu1', 'old_label': '2592.fu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.fu1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247747
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '64.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1', '32.c1', '32.d1'], 'contains': ['128.a1', '192.m1', '192.n1', '192.o1', '192.p1', '192.q1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [10405, 10368, 22752, 30964, 16080, 1728], 'label': '31104.fx.64.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.d1', 'old_label': '64.d1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.d1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
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id: 186247748
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.fv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.if1', '1296.ip1', '1296.ls1', '1296.lu1'], 'contains': ['5184.bd1', '5184.bv1', '7776.bd1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [5713, 6, 12096], 'label': '31104.fx.2592.fv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.gh1', 'old_label': '2592.fv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.fv1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247749
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.fw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.q1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.ig1', '864.ii1', '864.il1', '1296.bf1', '1296.bn1', '1296.ir1'], 'contains': ['5184.bh1', '5184.bp1', '5184.bw1', '7776.be1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [1, 18180, 10368], 'label': '31104.fx.2592.fw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.n1', 'old_label': '2592.fw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.fw1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247750
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.fx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.ig1', '864.ij1', '864.im2', '1296.bh1', '1296.bo1', '1296.is1'], 'contains': ['5184.bi1', '5184.bq1', '5184.bx1', '7776.be1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [20737, 18180, 12384], 'label': '31104.fx.2592.fx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.o1', 'old_label': '2592.fx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.fx1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247751
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.fx2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.ig1', '864.ik1', '864.im1', '1296.bg1', '1296.bp1', '1296.is1'], 'contains': ['5184.bi1', '5184.bq2', '5184.bx1', '7776.be1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [20737, 15588, 12384], 'label': '31104.fx.2592.fx2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.o1', 'old_label': '2592.fx2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.fx2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247752
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.fy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.ih1', '864.in1', '1296.bn1', '1296.gb1', '1296.lv1'], 'contains': ['5184.bh1', '5184.bs1', '5184.bw1', '7776.bf1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [20737, 2628, 22752], 'label': '31104.fx.2592.fy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.c1', 'old_label': '2592.fy1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.fy1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247753
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.fz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.ih1', '864.io1', '1296.bo1', '1296.bp1', '1296.gc1'], 'contains': ['5184.bi1', '5184.bt1', '5184.bx1', '7776.bf1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [20737, 2628, 12384], 'label': '31104.fx.2592.fz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.o1', 'old_label': '2592.fz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.fz1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247754
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.ga1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.ej1', '864.ii1', '864.ij1', '864.ik1', '1296.bd1'], 'contains': ['5184.bk1', '5184.bo1', '5184.by1', '7776.be1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [20737, 15588, 12940], 'label': '31104.fx.2592.ga1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1296.bd1', 'old_label': '2592.ga1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.ga1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247755
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.gb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.il1', '864.im1', '864.im2', '1296.bi1', '1296.bx1', '1296.ix1'], 'contains': ['5184.bj1', '5184.br1', '5184.bv1', '7776.be1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [20737, 18180, 1728], 'label': '31104.fx.2592.gb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.p1', 'old_label': '2592.gb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.gb1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247756
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2592.gc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.in1', '864.io1', '1296.bx1', '1296.gd1', '1296.lu1'], 'contains': ['5184.bj1', '5184.bu3', '5184.bv1', '7776.bf1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [20737, 2628, 1728], 'label': '31104.fx.2592.gc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.a1', 'old_label': '2592.gc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.gc1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247757
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3456.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.d1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1152.a1', '1152.h1', '1152.i1', '1152.j1', '1152.k1', '1728.d1', '1728.p1', '1728.ba1', '1728.bj1', '1728.bu1', '1728.cd1', '1728.cv1', '1728.cy1', '1728.dg1'], 'contains': ['10368.a1', '10368.b1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [22752, 10368], 'label': '31104.fx.3456.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '3456.a1', 'normal_contained_in': ['216.b1', '1152.a1'], 'normal_contains': ['10368.a1'], 'normalizer': '1.a1', 'old_label': '3456.a1', 'projective_image': '31104.fx', 'quotient_action_image': '4.2', 'quotient_action_kernel': '864.4679', 'quotient_action_kernel_order': 864, 'quotient_fusion': None, 'short_label': '3456.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247758
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '64.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1', '32.c1', '32.e1', '32.f1'], 'contains': ['128.a1', '192.s1', '192.t1', '192.u1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [1, 10368, 22752, 12096, 18580, 5712], 'label': '31104.fx.64.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.d1', 'old_label': '64.e1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.e1', 'subgroup_fusion': None, 'weyl_group': '1944.2342'}
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id: 186247759
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3456.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.bs1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1152.a1', '1152.b1', '1152.c1', '1728.a1', '1728.n1', '1728.o1', '1728.z1', '1728.bc1', '1728.bf1', '1728.bo1', '1728.ca1', '1728.ce1', '1728.cu1', '1728.cx1', '1728.cx2', '1728.da1'], 'contains': ['10368.a1', '10368.c1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [12096, 22752], 'label': '31104.fx.3456.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1152.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '3456.b1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3456.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247760
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3456.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.cy1', '1152.d1', '1152.e1', '1152.h1', '1728.b1', '1728.t1', '1728.cf1', '1728.cr1', '1728.dc1'], 'contains': ['10368.a1', '10368.d1', '10368.f1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [10924, 22752], 'label': '31104.fx.3456.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1', 'old_label': '3456.c1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3456.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247761
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3456.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.cz1', '864.ge1', '1152.d1', '1152.e1', '1152.i1', '1728.u1', '1728.bg1', '1728.bh1', '1728.bn1', '1728.cb1', '1728.cg1', '1728.dd1'], 'contains': ['10368.a1', '10368.e1', '10368.g1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [5712, 22752], 'label': '31104.fx.3456.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bc1', 'old_label': '3456.d1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3456.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247762
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3456.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.da1', '864.gf1', '1152.b1', '1152.e1', '1152.f1', '1152.i1', '1728.v1', '1728.bd1', '1728.bm1', '1728.bp1', '1728.bq1', '1728.ch1', '1728.de1'], 'contains': ['10368.a1', '10368.e1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [5712, 10368], 'label': '31104.fx.3456.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.d1', 'old_label': '3456.e1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3456.e1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 186247763
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3456.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.db1', '864.gg1', '1152.c1', '1152.d1', '1152.g1', '1152.i1', '1728.br1', '1728.bs1', '1728.df1'], 'contains': ['10368.a1', '10368.g1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [28464, 10368], 'label': '31104.fx.3456.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.f1', 'old_label': '3456.f1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3456.f1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247764
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3456.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bm1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.dd1', '1152.f1', '1152.g1', '1152.j1', '1728.c1', '1728.ci1'], 'contains': ['10368.a1', '10368.h1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [3412, 22752], 'label': '31104.fx.3456.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.o1', 'old_label': '3456.g1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3456.g1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247765
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3456.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.de1', '864.gh1', '864.gh2', '1152.b1', '1152.c1', '1152.k1', '1728.be1', '1728.bt1', '1728.cj1'], 'contains': ['10368.a1', '10368.i1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [29904, 10368], 'label': '31104.fx.3456.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.u1', 'old_label': '3456.h1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3456.h1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247766
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3456.h2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.de2', '864.gh3', '1152.f1', '1152.g1', '1152.k1', '1728.bi1', '1728.cc1', '1728.cj2'], 'contains': ['10368.a1', '10368.i1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [24268, 10368], 'label': '31104.fx.3456.h2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.x1', 'old_label': '3456.h2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3456.h2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247767
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3456.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1152.a1', '1152.l1', '1152.m1', '1728.e1', '1728.f1', '1728.g1', '1728.q1', '1728.r1', '1728.bb1', '1728.ck1', '1728.cw1', '1728.cw2', '1728.cw3', '1728.cz1', '1728.cz2', '1728.db1'], 'contains': ['10368.b1', '10368.c1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [12096, 12384], 'label': '31104.fx.3456.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1152.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '3456.i1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3456.i1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247768
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3456.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.dk1', '1152.h1', '1152.n1', '1152.p1', '1728.h1', '1728.w1', '1728.cl1', '1728.cs1', '1728.dh1'], 'contains': ['10368.b1', '10368.d1', '10368.f1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [10924, 2016], 'label': '31104.fx.3456.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1', 'old_label': '3456.j1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3456.j1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247769
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': ['432.oi1'], 'conjugacy_class_count': 1, 'contained_in': ['24.a1', '24.n1', '36.a1', '36.bs1', '36.cj1', '36.cm1', '36.cz1'], 'contains': ['144.bg1', '144.da1', '216.b1', '216.gw1', '216.hc1'], 'core': '72.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [16056, 22752, 12096, 18576, 10368, 18144, 15552], 'label': '31104.fx.72.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': ['24.a1', '36.a1'], 'normal_contains': ['216.b1', '1152.a1'], 'normalizer': '1.a1', 'old_label': '72.a1', 'projective_image': '31104.fx', 'quotient_action_image': '72.46', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '72.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186247770
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3456.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.dl1', '1152.h1', '1152.l1', '1152.o1', '1152.p1', '1728.i1', '1728.x1', '1728.cm1', '1728.ct1', '1728.di1'], 'contains': ['10368.b1', '10368.d1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [556, 12384], 'label': '31104.fx.3456.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1', 'old_label': '3456.k1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3456.k1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186247771
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3456.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.dm1', '864.dn1', '864.gk1', '1152.i1', '1152.n1', '1152.p1', '1728.y1', '1728.cn1', '1728.dj1'], 'contains': ['10368.b1', '10368.e1', '10368.g1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [5712, 12384], 'label': '31104.fx.3456.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.p1', 'old_label': '3456.l1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3456.l1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247772
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3456.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.dp1', '1152.h1', '1152.m1', '1152.n1', '1152.q1', '1728.j1', '1728.dk1'], 'contains': ['10368.b1', '10368.f1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [10924, 12384], 'label': '31104.fx.3456.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.c1', 'old_label': '3456.m1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3456.m1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
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id: 186247773
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3456.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.ds1', '1152.j1', '1152.o1', '1152.q1', '1728.m1', '1728.co1'], 'contains': ['10368.b1', '10368.h1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [24148, 12384], 'label': '31104.fx.3456.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.m1', 'old_label': '3456.n1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3456.n1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247774
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3456.n2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.dt1', '1152.j1', '1152.l1', '1152.m1', '1728.k1', '1728.l1', '1728.co2'], 'contains': ['10368.b1', '10368.h1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [13780, 2016], 'label': '31104.fx.3456.n2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.i1', 'old_label': '3456.n2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3456.n2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247775
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3456.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.du1', '864.dv1', '864.gl1', '1152.k1', '1152.o1', '1152.q1', '1728.cp1'], 'contains': ['10368.b1', '10368.i1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 384, 'diagramx': None, 'generators': [29904, 12384], 'label': '31104.fx.3456.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '192.o1', 'old_label': '3456.o1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3456.o1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247776
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3456.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.dw1', '864.dy1', '1152.d1', '1152.e1', '1152.n1', '1152.p1', '1728.dl1'], 'contains': ['10368.d1', '10368.e1', '10368.f1', '10368.g1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 384, 'diagramx': None, 'generators': [30964, 28464], 'label': '31104.fx.3456.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '192.u1', 'old_label': '3456.p1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3456.p1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247777
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3456.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.dx1', '864.dz1', '1152.d1', '1152.n1', '1152.p1', '1728.dm1'], 'contains': ['10368.d1', '10368.f1', '10368.g1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [20596, 28464], 'label': '31104.fx.3456.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '192.u1', 'old_label': '3456.q1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3456.q1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247778
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3456.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.ea1', '1152.e1', '1152.p1', '1728.s1', '1728.bk1', '1728.bv1', '1728.cq1', '1728.dn1'], 'contains': ['10368.d1', '10368.e1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [8212, 5712], 'label': '31104.fx.3456.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bc1', 'old_label': '3456.r1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3456.r1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247779
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3456.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.eb1', '1152.d1', '1152.p1', '1728.bw1', '1728.do1'], 'contains': ['10368.d1', '10368.g1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [18580, 28464], 'label': '31104.fx.3456.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.ba1', 'old_label': '3456.s1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3456.s1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247780
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '9.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3.a1', '3.b1'], 'contains': ['18.l1', '18.n1', '18.p1', '18.x1', '18.ba1', '18.bg1', '18.bj1', '27.b1', '27.c1', '27.e1', '36.dj1'], 'core': '36.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [5713, 2592, 22752, 10368, 15552, 24198, 15628, 18576, 2664, 36], 'label': '31104.fx.9.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '9.c1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.c1', 'subgroup_fusion': None, 'weyl_group': '3456.de'}
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id: 186247801
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.kg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.cs1', '1296.ct1', '1296.cu1', '1296.cv1', '1944.d1', '1944.h1', '1944.i1', '1944.j1', '1944.k1', '1944.l1', '1944.w1'], 'contains': ['7776.j1', '7776.m1', '7776.t1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [17371, 18648], 'label': '31104.fx.3888.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '3888.o1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.o1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247781
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['24.a1', '24.b1', '24.p1', '36.b1', '36.bo1', '36.bt1', '36.ca1', '36.ck1', '36.co1', '36.df1'], 'contains': ['216.a1', '216.b1', '216.gy1', '216.gz1', '216.hf1', '288.bl1', '288.cs1'], 'core': '72.b1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [76, 2592, 18576, 22752, 15552, 10368, 2664], 'label': '31104.fx.72.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.b1', 'normal_contained_in': ['24.a1', '24.b1', '36.b1'], 'normal_contains': ['216.a1', '216.b1'], 'normalizer': '1.a1', 'old_label': '72.b1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.b1', 'subgroup_fusion': None, 'weyl_group': '3456.di'}
-
id: 186247782
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3456.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.ec1', '1152.d1', '1152.e1', '1152.n1', '1728.bx1', '1728.by1', '1728.dp1'], 'contains': ['10368.e1', '10368.f1', '10368.g1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [18580, 5712], 'label': '31104.fx.3456.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.ba1', 'old_label': '3456.t1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3456.t1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247783
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3456.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.ed1', '1152.e1', '1152.n1', '1728.bl1', '1728.dq1'], 'contains': ['10368.e1', '10368.f1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [30964, 5712], 'label': '31104.fx.3456.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.z1', 'old_label': '3456.u1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3456.u1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247784
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3456.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.ee1', '1152.d1', '1152.n1', '1728.bz1', '1728.dr2'], 'contains': ['10368.f1', '10368.g1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [28948, 28464], 'label': '31104.fx.3456.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.ba1', 'old_label': '3456.v1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3456.v1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247785
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3456.v2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.ee2', '1152.d1', '1152.n1', '1728.dr1'], 'contains': ['10368.f1', '10368.g1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [10228, 28464], 'label': '31104.fx.3456.v2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '192.u1', 'old_label': '3456.v2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3456.v2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247786
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.a1', '1296.b1', '1296.c1', '1296.d1', '1296.e1', '1296.f1', '1296.g1', '1944.b1', '1944.v1', '1944.bh1'], 'contains': ['7776.a1', '7776.b1', '7776.f1', '7776.l1', '7776.p1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [36, 16056, 15552], 'label': '31104.fx.3888.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.h1', 'old_label': '3888.a1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247787
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.cx1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.h1', '1296.i1', '1296.j1', '1296.k1', '1944.b1', '1944.c1', '1944.bi1'], 'contains': ['7776.a1', '7776.c1', '7776.h1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [10405, 16056], 'label': '31104.fx.3888.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cr1', 'old_label': '3888.b1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247788
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.l1', '1296.m1', '1296.n1', '1296.o1', '1296.p1', '1296.p2', '1296.q1', '1296.r1', '1296.r2', '1944.v1', '1944.z1', '1944.bj1'], 'contains': ['7776.a1', '7776.d1', '7776.f1', '7776.p1', '7776.r1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [18612, 16056, 15552], 'label': '31104.fx.3888.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.ba1', 'old_label': '3888.c1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 186247789
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.s1', '1296.t1', '1296.u1', '1296.v1', '1296.w1', '1296.x1', '1296.y1', '1944.c1', '1944.z1', '1944.bh1'], 'contains': ['7776.a1', '7776.d1', '7776.e1', '7776.p1', '7776.q1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [2628, 16056, 15552], 'label': '31104.fx.3888.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.h1', 'old_label': '3888.d1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247790
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.cp1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.z1', '1296.ba1', '1296.bb1', '1296.bc1', '1944.b1', '1944.c1', '1944.bk1'], 'contains': ['7776.a1', '7776.g1', '7776.i1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1, 16056], 'label': '31104.fx.3888.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cp1', 'old_label': '3888.e1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.e1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247791
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.bd1', '1296.bf1', '1296.bg1', '1296.bh1', '1296.bi1', '1944.b1', '1944.e1', '1944.bf1'], 'contains': ['7776.b1', '7776.c1', '7776.g1', '7776.z1', '7776.be1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [20737, 36, 18144], 'label': '31104.fx.3888.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.w1', 'old_label': '3888.f1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247792
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bc1'], 'contains': ['144.a1', '144.b1', '144.e1', '144.j1', '144.k1', '144.o1', '144.u1', '216.c1', '216.d1', '216.e1', '216.f1'], 'core': '576.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1, 22752, 12096, 36, 10368, 16056, 15552], 'label': '31104.fx.72.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bc1', 'old_label': '72.c1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.c1', 'subgroup_fusion': None, 'weyl_group': '216.171'}
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id: 186247793
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.be1', '1296.bj1', '1296.bk1', '1296.bl1', '1296.bm1', '1944.b1', '1944.g1', '1944.bf1'], 'contains': ['7776.b1', '7776.h1', '7776.i1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [5257, 36], 'label': '31104.fx.3888.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.w1', 'old_label': '3888.g1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247794
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.bn1', '1296.bo1', '1296.bp1', '1296.bx1', '1944.c1', '1944.e1', '1944.bg1'], 'contains': ['7776.c1', '7776.d1', '7776.g1', '7776.be1', '7776.bf1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [20737, 2628, 18144], 'label': '31104.fx.3888.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.w1', 'old_label': '3888.h1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.h1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247795
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.bq1', '1296.br1', '1296.bs1', '1296.bw1', '1296.by1', '1944.c1', '1944.o1', '1944.bf1'], 'contains': ['7776.c1', '7776.e1', '7776.i1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [5257, 18252], 'label': '31104.fx.3888.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.w1', 'old_label': '3888.i1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.i1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247796
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.bt1', '1296.bu1', '1296.bv1', '1296.bz1', '1944.b1', '1944.o1', '1944.bg1'], 'contains': ['7776.c1', '7776.f1', '7776.i1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [5257, 15660], 'label': '31104.fx.3888.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.w1', 'old_label': '3888.j1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.j1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247797
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.cb1', '1296.cc1', '1296.cd1', '1296.ce1', '1944.c1', '1944.g1', '1944.bg1'], 'contains': ['7776.d1', '7776.h1', '7776.i1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [5257, 2628], 'label': '31104.fx.3888.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.w1', 'old_label': '3888.k1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.k1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247798
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.ca1', '1296.cf1', '1296.cg1', '1296.ch1', '1296.ci1', '1944.c1', '1944.q1', '1944.bf1'], 'contains': ['7776.e1', '7776.g1', '7776.h1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [20737, 18252], 'label': '31104.fx.3888.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.w1', 'old_label': '3888.l1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.l1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247799
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.cj1', '1296.ck1', '1296.cl1', '1296.cm1', '1944.b1', '1944.q1', '1944.bg1'], 'contains': ['7776.f1', '7776.g1', '7776.h1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [20737, 15660], 'label': '31104.fx.3888.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.w1', 'old_label': '3888.m1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.m1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247800
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.cn1', '1296.co1', '1296.cp1', '1296.cq1', '1296.cr1', '1944.d1', '1944.e1', '1944.f1', '1944.g1', '1944.v1', '1944.bh1'], 'contains': ['7776.b1', '7776.d1', '7776.j1', '7776.l1', '7776.q1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [36, 18144, 16056], 'label': '31104.fx.3888.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '3888.n1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.n1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 186247900
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.bn1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.kn1', '1728.bn1', '1728.bs1', '1728.bw1', '1728.by1', '1728.bz1', '2592.fu1'], 'contains': ['10368.g1', '15552.e1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 1728, 'diagramx': None, 'generators': [26047, 28464], 'label': '31104.fx.5184.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '864.ie1', 'old_label': '5184.bb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.bb1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 186247802
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.in1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.cw1', '1296.cx1', '1296.cy1', '1296.cz1', '1944.d1', '1944.h1', '1944.i1', '1944.j1', '1944.m1', '1944.n1', '1944.x1'], 'contains': ['7776.j1', '7776.n1', '7776.v1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [6, 18144], 'label': '31104.fx.3888.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '3888.p1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.p1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247803
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bc1'], 'contains': ['144.b1', '144.d1', '144.e1', '144.m1', '144.n1', '144.s1', '144.t1', '216.g1', '216.h1', '216.i1', '216.j1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1, 22752, 12096, 2628, 10368, 16056, 15552], 'label': '31104.fx.72.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bc1', 'old_label': '72.d1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.d1', 'subgroup_fusion': None, 'weyl_group': '216.171'}
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id: 186247804
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.da1', '1296.db1', '1296.dc1', '1944.e1', '1944.h1', '1944.o1', '1944.p1', '1944.y1', '1944.bi1'], 'contains': ['7776.c1', '7776.j1', '7776.o1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [10405, 15552, 2592], 'label': '31104.fx.3888.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '3888.q1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.q1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
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id: 186247805
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.dd1', '1296.de1', '1296.de2', '1296.df1', '1296.dg1', '1296.dg2', '1296.dh1', '1944.o1', '1944.q1', '1944.r1', '1944.s1', '1944.z1', '1944.bh1', '1944.bj1'], 'contains': ['7776.d1', '7776.e1', '7776.f1', '7776.j1', '7776.p1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [15588, 18144, 16056], 'label': '31104.fx.3888.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.h1', 'old_label': '3888.r1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.r1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247806
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.di1', '1296.dj1', '1296.dk1', '1296.dl1', '1296.dm1', '1944.i1', '1944.p1', '1944.t1', '1944.u1', '1944.v1', '1944.bj1'], 'contains': ['7776.f1', '7776.j1', '7776.r1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [468, 18144, 16056], 'label': '31104.fx.3888.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '3888.s1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.s1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247807
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.dn1', '1296.do1', '1296.dp1', '1944.e1', '1944.k1', '1944.m1', '1944.q1', '1944.t1', '1944.ba1', '1944.bk1'], 'contains': ['7776.g1', '7776.j1', '7776.s1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1, 15552, 2592], 'label': '31104.fx.3888.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '3888.t1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.t1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
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id: 186247808
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.dq1', '1296.du1', '1296.dz1', '1944.f1', '1944.j1', '1944.r1', '1944.t1', '1944.y1', '1944.bl1'], 'contains': ['7776.j1', '7776.u1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [10837, 18144], 'label': '31104.fx.3888.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '3888.u1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.u1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
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id: 186247809
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.dr1', '1296.dv1', '1296.dw1', '1296.ea1', '1944.g1', '1944.q1', '1944.s1', '1944.u1', '1944.bc1', '1944.bi1', '1944.bl1'], 'contains': ['7776.h1', '7776.j1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [26461, 2592], 'label': '31104.fx.3888.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bd1', 'old_label': '3888.v1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.v1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247810
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.ds1', '1296.dx1', '1296.eb1', '1944.f1', '1944.l1', '1944.n1', '1944.p1', '1944.s1', '1944.ba1', '1944.bm1'], 'contains': ['7776.j1', '7776.w1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [433, 15552], 'label': '31104.fx.3888.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '3888.w1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.w1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
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id: 186247811
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.w1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.dt1', '1296.dy1', '1296.dy2', '1296.ec1', '1944.g1', '1944.o1', '1944.r1', '1944.u1', '1944.be1', '1944.bk1', '1944.bm1'], 'contains': ['7776.i1', '7776.j1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [16057, 2592], 'label': '31104.fx.3888.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '3888.x1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.x1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247812
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.ed1', '1296.ee1', '1296.ef1', '1296.eg1', '1296.eh1', '1944.a1', '1944.v1', '1944.w1', '1944.x1', '1944.y1', '1944.z1', '1944.ba1', '1944.bb1', '1944.bc1', '1944.bd1', '1944.be1'], 'contains': ['7776.a1', '7776.j1', '7776.x1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [18576, 18144, 16056], 'label': '31104.fx.3888.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1944.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '3888.y1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.y1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247813
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.de1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.ei1', '1296.ej1', '1296.ek1', '1296.el1', '1296.em1', '1296.en1', '1296.eo1', '1944.bf1', '1944.bh1'], 'contains': ['7776.b1', '7776.e1', '7776.k1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [36, 3096, 15552], 'label': '31104.fx.3888.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.p1', 'old_label': '3888.z1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.z1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247814
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.c1', '36.d1', '36.g1'], 'contains': ['144.v1', '144.w1', '144.x1', '144.dh1', '144.dj1', '144.dp1', '144.dx1', '216.k1', '216.l1', '216.m1', '216.n1'], 'core': '576.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [6, 10368, 12096, 36, 22752, 18144, 16056], 'label': '31104.fx.72.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '72.e1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.e1', 'subgroup_fusion': None, 'weyl_group': '432.759'}
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id: 186247815
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.cx1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.ep1', '1296.eq1', '1296.er1', '1296.es1', '1296.et1', '1296.eu1', '1296.ev1', '1296.ew1', '1296.ex1', '1296.ey1', '1944.bf1', '1944.bg1', '1944.bi1'], 'contains': ['7776.c1', '7776.h1', '7776.k1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [10405, 3096], 'label': '31104.fx.3888.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cr1', 'old_label': '3888.ba1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.ba1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247816
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.ez1', '1296.fa1', '1296.fb1', '1296.fc1', '1296.fd1', '1296.fd2', '1944.bg1', '1944.bh1', '1944.bj1'], 'contains': ['7776.d1', '7776.f1', '7776.k1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [3060, 3096, 15552], 'label': '31104.fx.3888.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.q1', 'old_label': '3888.bb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bb1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247817
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.cp1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.fe1', '1296.ff1', '1296.fg1', '1296.fh1', '1296.fi1', '1296.fj1', '1296.fk1', '1296.fl1', '1296.fm1', '1296.fn1', '1944.bf1', '1944.bg1', '1944.bk1'], 'contains': ['7776.g1', '7776.i1', '7776.k1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1, 3096], 'label': '31104.fx.3888.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cp1', 'old_label': '3888.bc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bc1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247818
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.fo1', '1296.fp1', '1296.fq1', '1296.fr1', '1296.fs1', '1296.ft1', '1296.fu1', '1296.fv1', '1296.fw1', '1944.a1', '1944.bh1', '1944.bi1', '1944.bj1', '1944.bk1', '1944.bl1', '1944.bm1'], 'contains': ['7776.a1', '7776.j1', '7776.k1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [18144, 3096, 15552], 'label': '31104.fx.3888.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1944.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '3888.bd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bd1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247819
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.bg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.fx1', '1296.fy1', '1296.fz1', '1296.ga1', '1944.d1', '1944.bn1', '1944.bo1', '1944.bp1', '1944.bq1', '1944.ch1', '1944.ci1'], 'contains': ['7776.l1', '7776.m1', '7776.n1', '7776.y1', '7776.bb1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [19135, 36, 18576], 'label': '31104.fx.3888.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '3888.be1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.be1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247820
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.gb1', '1296.gc1', '1296.gd1', '1944.e1', '1944.bn1', '1944.bp1', '1944.br1', '1944.cj1'], 'contains': ['7776.l1', '7776.o1', '7776.s1', '7776.z1', '7776.bf1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [20737, 36, 2592], 'label': '31104.fx.3888.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '3888.bf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bf1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 186247821
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.bf1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.ge1', '1296.gf1', '1296.gi1', '1296.gj1', '1944.d1', '1944.bn1', '1944.bo1', '1944.br1', '1944.bs1', '1944.ch1', '1944.ck1'], 'contains': ['7776.l1', '7776.t1', '7776.v1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [3943, 36], 'label': '31104.fx.3888.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '3888.bg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bg1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247822
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.gg1', '1296.gh1', '1296.gk1', '1944.f1', '1944.bo1', '1944.bq1', '1944.bs1', '1944.cj1'], 'contains': ['7776.l1', '7776.u1', '7776.w1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [5617, 36], 'label': '31104.fx.3888.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '3888.bh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bh1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247823
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.gl1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.gl1', '1296.gn1', '1296.hj1', '1944.h1', '1944.bp1', '1944.bt1', '1944.bv1', '1944.bz1', '1944.cm1', '1944.cp1'], 'contains': ['7776.m1', '7776.n1', '7776.o1', '7776.ba1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [26485, 12138, 18576], 'label': '31104.fx.3888.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '3888.bi1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bi1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247824
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.ci1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.go1', '1296.gp1', '1296.gq1', '1296.hi1', '1944.i1', '1944.bv1', '1944.bw1', '1944.bz1', '1944.ca1', '1944.ci1', '1944.cl1'], 'contains': ['7776.m1', '7776.n1', '7776.r1', '7776.bb1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [19135, 2628, 18576], 'label': '31104.fx.3888.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '3888.bj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bj1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247825
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1', '36.h1', '36.bc1'], 'contains': ['144.j1', '144.m1', '144.v1', '144.y1', '144.bb1', '144.di1', '144.ee1', '216.o1', '216.p1', '216.q1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1, 22752, 12096, 36, 10368, 18144, 2592], 'label': '31104.fx.72.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '72.f1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.f1', 'subgroup_fusion': None, 'weyl_group': '864.4406'}
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id: 186247826
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.gm1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.gm1', '1296.gr1', '1296.hk1', '1944.j1', '1944.bq1', '1944.bu1', '1944.bw1', '1944.ca1', '1944.cm1', '1944.cp1'], 'contains': ['7776.m1', '7776.n1', '7776.u1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [29077, 12138], 'label': '31104.fx.3888.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '3888.bk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bk1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247827
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.gd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.gs1', '1296.gt1', '1296.hl1', '1944.h1', '1944.bn1', '1944.bx1', '1944.bz1', '1944.cb1', '1944.cn1', '1944.cp1'], 'contains': ['7776.m1', '7776.o1', '7776.v1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [26485, 14802], 'label': '31104.fx.3888.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '3888.bl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bl1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247828
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cj1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.gu1', '1296.gv1', '1296.gw1', '1296.hm1', '1944.d1', '1944.bt1', '1944.bu1', '1944.cb1', '1944.cc1', '1944.cl1', '1944.cq1'], 'contains': ['7776.m1', '7776.q1', '7776.v1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [6054, 18180], 'label': '31104.fx.3888.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '3888.bm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bm1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247829
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.ch1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.gx1', '1296.gy1', '1296.gz1', '1296.hn1', '1944.i1', '1944.bx1', '1944.by1', '1944.bz1', '1944.ca1', '1944.ch1', '1944.cq1'], 'contains': ['7776.m1', '7776.r1', '7776.v1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [3943, 16092], 'label': '31104.fx.3888.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '3888.bn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bn1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247830
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.ge1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.ha1', '1296.hb1', '1296.ho1', '1944.k1', '1944.bn1', '1944.bt1', '1944.bw1', '1944.by1', '1944.co1', '1944.cr1'], 'contains': ['7776.m1', '7776.s1', '7776.t1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 14730], 'label': '31104.fx.3888.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '3888.bo1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bo1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247831
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.gg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.hc1', '1296.he1', '1296.hp1', '1944.l1', '1944.bo1', '1944.bu1', '1944.bv1', '1944.bx1', '1944.co1', '1944.cr1'], 'contains': ['7776.m1', '7776.t1', '7776.w1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [8305, 14730], 'label': '31104.fx.3888.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '3888.bp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bp1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247832
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.gf1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.hd1', '1296.hf1', '1296.hq1', '1944.j1', '1944.bo1', '1944.by1', '1944.ca1', '1944.cc1', '1944.cn1', '1944.cp1'], 'contains': ['7776.m1', '7776.u1', '7776.v1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [29077, 14802], 'label': '31104.fx.3888.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '3888.bq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bq1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247833
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.gh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.hg1', '1296.hr1', '1944.k1', '1944.bp1', '1944.ca1', '1944.cb1', '1944.cr1'], 'contains': ['7776.m1', '7776.s1', '7776.bc1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [5713, 12138, 18576], 'label': '31104.fx.3888.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '3888.br1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.br1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247834
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.gi1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.hh1', '1296.hs1', '1944.l1', '1944.bq1', '1944.bz1', '1944.cc1', '1944.cr1'], 'contains': ['7776.m1', '7776.w1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [8305, 12138], 'label': '31104.fx.3888.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '3888.bs1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bs1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247835
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.gj1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.ht1', '1296.hz1', '1296.ia1', '1944.h1', '1944.bn1', '1944.bv1', '1944.cd1', '1944.cf1', '1944.cm1', '1944.cs1'], 'contains': ['7776.n1', '7776.o1', '7776.t1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [26485, 14730], 'label': '31104.fx.3888.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '3888.bt1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bt1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247836
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.d1', '36.h1', '36.bd1'], 'contains': ['144.v1', '144.bc1', '144.be1', '144.dk1', '144.eh1', '216.r1', '216.t1', '216.v1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [433, 22752, 12096, 36, 10368, 15552, 2592], 'label': '31104.fx.72.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '72.g1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.g1', 'subgroup_fusion': None, 'weyl_group': '864.4406'}
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id: 186247837
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cj1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.hu1', '1296.ib1', '1296.ic1', '1296.id1', '1944.d1', '1944.bt1', '1944.bu1', '1944.cf1', '1944.cg1', '1944.cl1', '1944.cu1'], 'contains': ['7776.n1', '7776.q1', '7776.t1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [19135, 18684], 'label': '31104.fx.3888.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '3888.bu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bu1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247838
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.ch1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.hv1', '1296.ie1', '1296.if1', '1296.ig1', '1944.i1', '1944.bv1', '1944.bw1', '1944.cd1', '1944.ce1', '1944.ch1', '1944.cu1'], 'contains': ['7776.n1', '7776.r1', '7776.t1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [19135, 16092], 'label': '31104.fx.3888.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '3888.bv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bv1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247839
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.bn1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.hw1', '1296.ih1', '1296.ii1', '1944.m1', '1944.bn1', '1944.bt1', '1944.ca1', '1944.ce1', '1944.ct1', '1944.cv1'], 'contains': ['7776.n1', '7776.s1', '7776.v1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [5713, 2598], 'label': '31104.fx.3888.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '3888.bw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bw1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247840
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.gk1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.hx1', '1296.ij1', '1296.il1', '1944.j1', '1944.bo1', '1944.bw1', '1944.ce1', '1944.cg1', '1944.cm1', '1944.cs1'], 'contains': ['7776.n1', '7776.t1', '7776.u1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [29077, 14730], 'label': '31104.fx.3888.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '3888.bx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bx1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 186247841
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.bo1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.hy1', '1296.ik1', '1296.im1', '1944.n1', '1944.bo1', '1944.bu1', '1944.bz1', '1944.cd1', '1944.ct1', '1944.cv1'], 'contains': ['7776.n1', '7776.v1', '7776.w1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [8305, 2598], 'label': '31104.fx.3888.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '3888.by1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.by1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247842
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.bp1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.in1', '1296.ip1', '1944.m1', '1944.bp1', '1944.bw1', '1944.cf1', '1944.cv1'], 'contains': ['7776.n1', '7776.s1', '7776.bd1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [5713, 6, 18576], 'label': '31104.fx.3888.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '3888.bz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bz1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247843
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.bq1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.io1', '1296.iq1', '1944.n1', '1944.bq1', '1944.bv1', '1944.cg1', '1944.cv1'], 'contains': ['7776.n1', '7776.w1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [8305, 6], 'label': '31104.fx.3888.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '3888.ca1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.ca1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247844
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.ir1', '1296.is1', '1296.ix1', '1944.e1', '1944.bt1', '1944.cb1', '1944.cf1', '1944.cw1'], 'contains': ['7776.o1', '7776.q1', '7776.s1', '7776.be1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [20737, 15588, 2592], 'label': '31104.fx.3888.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '3888.cb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.cb1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247845
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.it1', '1296.it2', '1296.iu1', '1296.iy1', '1944.p1', '1944.bv1', '1944.bx1', '1944.bz1', '1944.cd1', '1944.cj1', '1944.cw1'], 'contains': ['7776.o1', '7776.r1', '7776.w1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [5617, 468], 'label': '31104.fx.3888.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '3888.cc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.cc1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247846
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.gn1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.iv1', '1296.iw1', '1296.iz1', '1944.h1', '1944.br1', '1944.bt1', '1944.bx1', '1944.cd1', '1944.cn1', '1944.cs1'], 'contains': ['7776.o1', '7776.t1', '7776.v1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [26485, 12210], 'label': '31104.fx.3888.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '3888.cd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.cd1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247847
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.j1', '36.bc1', '36.bd1'], 'contains': ['144.k1', '144.s1', '144.v1', '144.bd1', '144.bf1', '216.s1', '216.u1', '216.w1', '216.x1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [16057, 22752, 12096, 36, 10368, 2592, 15552], 'label': '31104.fx.72.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '72.h1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.h1', 'subgroup_fusion': None, 'weyl_group': '432.768'}
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id: 186247848
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.ja1', '1296.jb1', '1296.jc1', '1944.f1', '1944.bu1', '1944.cc1', '1944.cg1', '1944.cw1'], 'contains': ['7776.q1', '7776.u1', '7776.w1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [5617, 15588], 'label': '31104.fx.3888.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '3888.ce1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.ce1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247849
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.jd1', '1296.je1', '1296.je2', '1296.jf1', '1944.t1', '1944.bw1', '1944.by1', '1944.ca1', '1944.ce1', '1944.cj1', '1944.cw1'], 'contains': ['7776.r1', '7776.s1', '7776.u1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [20737, 468], 'label': '31104.fx.3888.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '3888.cf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.cf1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247850
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.ck1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.jg1', '1296.jh1', '1296.ji1', '1296.jj1', '1944.i1', '1944.bx1', '1944.by1', '1944.cd1', '1944.ce1', '1944.ck1', '1944.cl1'], 'contains': ['7776.r1', '7776.t1', '7776.v1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [3943, 2628], 'label': '31104.fx.3888.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '3888.cg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.cg1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247851
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.go1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.jk1', '1296.jm1', '1944.k1', '1944.br1', '1944.ce1', '1944.cf1', '1944.co1'], 'contains': ['7776.s1', '7776.t1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [5713, 12210], 'label': '31104.fx.3888.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '3888.ch1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.ch1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247852
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.jl1', '1296.jn1', '1944.m1', '1944.br1', '1944.by1', '1944.cb1', '1944.ct1'], 'contains': ['7776.s1', '7776.v1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [5713, 78], 'label': '31104.fx.3888.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '3888.ci1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.ci1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247853
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.gp1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.jo1', '1296.jp1', '1296.js1', '1944.j1', '1944.bs1', '1944.bu1', '1944.by1', '1944.ce1', '1944.cn1', '1944.cs1'], 'contains': ['7776.t1', '7776.u1', '7776.v1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [10069, 78], 'label': '31104.fx.3888.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '3888.cj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.cj1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247854
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.gq1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.jq1', '1296.jt1', '1944.l1', '1944.bs1', '1944.cd1', '1944.cg1', '1944.co1'], 'contains': ['7776.t1', '7776.w1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [8305, 12210], 'label': '31104.fx.3888.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '3888.ck1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.ck1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247855
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.bs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.jr1', '1296.ju1', '1944.n1', '1944.bs1', '1944.bx1', '1944.cc1', '1944.ct1'], 'contains': ['7776.v1', '7776.w1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [8305, 78], 'label': '31104.fx.3888.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.b1', 'old_label': '3888.cl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.cl1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247856
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.jv1', '1296.jw1', '1296.jw2', '1296.jx1', '1296.jy1', '1296.jz1', '1944.v1', '1944.ch1', '1944.ci1', '1944.cj1', '1944.ck1'], 'contains': ['7776.l1', '7776.r1', '7776.x1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [36, 16056, 432], 'label': '31104.fx.3888.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '3888.cm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.cm1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247857
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.jz1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.ka1', '1296.kb1', '1296.kc1', '1296.kh1', '1296.ki1', '1944.w1', '1944.ch1', '1944.cl1', '1944.cm1', '1944.cn1', '1944.co1', '1944.cr1'], 'contains': ['7776.m1', '7776.t1', '7776.x1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [17371, 16056], 'label': '31104.fx.3888.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '3888.cn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.cn1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247858
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.c1', '36.e1', '36.k1'], 'contains': ['144.w1', '144.x1', '144.y1', '144.dl1', '144.do1', '144.dw1', '144.eg1', '216.y1', '216.bb1', '216.bg1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [26485, 12096, 18576, 6, 22752, 18648, 10368], 'label': '31104.fx.72.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '72.i1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.i1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186247859
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.jy1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.kd1', '1296.ke1', '1296.kf1', '1296.kg1', '1296.kj1', '1944.w1', '1944.ci1', '1944.cp1', '1944.cq1', '1944.cr1'], 'contains': ['7776.m1', '7776.x1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [12138, 16056, 18576], 'label': '31104.fx.3888.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '3888.co1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.co1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 186247860
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.ig1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.kk1', '1296.ko1', '1296.kp1', '1296.kq1', '1296.kr1', '1296.ks1', '1296.kt1', '1296.kt2', '1944.x1', '1944.ch1', '1944.cl1', '1944.cp1', '1944.cs1', '1944.ct1', '1944.cv1'], 'contains': ['7776.n1', '7776.v1', '7776.x1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [26047, 16056], 'label': '31104.fx.3888.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '3888.cp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.cp1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 186247861
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.im1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.kl1', '1296.km1', '1296.kn1', '1296.ku1', '1296.kv1', '1944.x1', '1944.ci1', '1944.cm1', '1944.cu1', '1944.cv1'], 'contains': ['7776.n1', '7776.x1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [6, 16056, 18576], 'label': '31104.fx.3888.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '3888.cq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.cq1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186247862
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.n1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.kw1', '1296.kw2', '1296.kx1', '1296.ky1', '1296.kz1', '1296.la1', '1944.y1', '1944.cj1', '1944.cm1', '1944.cn1', '1944.cp1', '1944.cs1', '1944.cw1'], 'contains': ['7776.o1', '7776.u1', '7776.x1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [10405, 3024], 'label': '31104.fx.3888.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '3888.cr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.cr1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247863
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.ba1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.lb1', '1296.lb2', '1296.lc1', '1296.ld1', '1296.ld2', '1296.le1', '1296.le2', '1944.v1', '1944.z1', '1944.cl1', '1944.cq1', '1944.cu1', '1944.cw1', '1944.cx1'], 'contains': ['7776.p1', '7776.q1', '7776.r1', '7776.x1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [18180, 16056, 432], 'label': '31104.fx.3888.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '3888.cs1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.cs1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247864
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.lf1', '1296.lg1', '1296.lg2', '1296.lh1', '1296.li1', '1296.lj1', '1944.ba1', '1944.cj1', '1944.co1', '1944.cr1', '1944.ct1', '1944.cv1', '1944.cw1'], 'contains': ['7776.s1', '7776.w1', '7776.x1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1, 18576], 'label': '31104.fx.3888.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '3888.ct1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.ct1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 186247865
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.ki1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.lk1', '1296.ll1', '1296.lo1', '1296.lp1', '1944.w1', '1944.bb1', '1944.ck1', '1944.co1', '1944.cs1', '1944.cu1', '1944.cx1'], 'contains': ['7776.t1', '7776.x1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [30282, 18576], 'label': '31104.fx.3888.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '3888.cu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.cu1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
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id: 186247866
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.ir1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.lm1', '1296.ln1', '1296.lq1', '1296.lq2', '1944.x1', '1944.bd1', '1944.ck1', '1944.cn1', '1944.cq1', '1944.ct1', '1944.cx1'], 'contains': ['7776.v1', '7776.x1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [10855, 2592], 'label': '31104.fx.3888.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '3888.cv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.cv1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
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id: 186247867
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.bp1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.lr1', '1296.ls1', '1296.lt1', '1944.bp1'], 'contains': ['7776.y1', '7776.z1', '7776.ba1', '7776.bc1', '7776.bd1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': None, 'generators': [5713, 24198, 36], 'label': '31104.fx.3888.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1944.bp1', 'old_label': '3888.cw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.cw1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 186247868
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3888.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.bp1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.lu1', '1296.lv1', '1944.bp1'], 'contains': ['7776.ba1', '7776.bb1', '7776.bc1', '7776.bd1', '7776.bf1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': None, 'generators': [5713, 24198, 18612], 'label': '31104.fx.3888.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1944.bp1', 'old_label': '3888.cx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.cx1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 186247869
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.e1', '36.f1', '36.g1'], 'contains': ['144.w1', '144.x1', '144.ba1', '144.dm1', '144.dq1', '144.dy1', '144.ej1', '216.ba1', '216.bc1', '216.bd1', '216.be1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [6, 10368, 12096, 18612, 22752, 18144, 16056], 'label': '31104.fx.72.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '72.j1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.j1', 'subgroup_fusion': None, 'weyl_group': '432.759'}
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id: 186247870
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.q1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1728.a1', '1728.b1', '1728.c1', '1728.d1', '2592.a1', '2592.i1', '2592.n1', '2592.u1', '2592.z1', '2592.be1', '2592.bk1', '2592.bp1', '2592.bq1', '2592.cb1', '2592.cg1'], 'contains': ['10368.a1', '15552.a1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [18144, 14400], 'label': '31104.fx.5184.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '648.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '5184.a1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247871
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1728.d1', '1728.e1', '1728.f1', '1728.i1', '1728.j1', '1728.k1', '1728.l1', '2592.b1', '2592.j1', '2592.o1', '2592.v1', '2592.ba1', '2592.bf1', '2592.bl1', '2592.br1', '2592.bt1', '2592.cc1', '2592.ch1'], 'contains': ['10368.b1', '15552.a1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [3096, 12384], 'label': '31104.fx.5184.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '5184.b1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247872
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1728.d1', '1728.g1', '1728.h1', '1728.m1', '2592.c1', '2592.k1', '2592.p1', '2592.w1', '2592.bb1', '2592.bg1', '2592.bm1', '2592.bs1', '2592.bu1', '2592.cc1', '2592.ci1'], 'contains': ['10368.b1', '15552.a1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [18144, 12384], 'label': '31104.fx.5184.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '5184.c1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247873
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.cz1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1728.a1', '1728.e1', '1728.g1', '2592.e1', '2592.f1', '2592.l1', '2592.q1', '2592.x1', '2592.x2', '2592.bc1', '2592.bh1', '2592.bh2', '2592.bj1', '2592.bv1', '2592.bw1', '2592.cd1', '2592.ce1', '2592.cj1'], 'contains': ['10368.c1', '15552.a1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [18648, 12096], 'label': '31104.fx.5184.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '5184.d1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247874
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1728.a1', '1728.f1', '1728.g1', '2592.d1', '2592.g1', '2592.m1', '2592.y1', '2592.y2', '2592.bd1', '2592.bi1', '2592.bi2', '2592.ce1', '2592.cf1', '2592.cj1'], 'contains': ['10368.c1', '15552.a1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [18144, 12096], 'label': '31104.fx.5184.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1', 'old_label': '5184.e1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247875
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.bl1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.ft1', '1728.b1', '1728.h1', '1728.i1', '2592.h1', '2592.r1', '2592.t1', '2592.bn1', '2592.bx1', '2592.by1', '2592.ck1'], 'contains': ['10368.d1', '15552.a1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [3096, 24460], 'label': '31104.fx.5184.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bj1', 'old_label': '5184.f1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247876
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.fu1', '1728.b1', '1728.h1', '1728.j1', '2592.bo1', '2592.bz1', '2592.cn1'], 'contains': ['10368.f1', '15552.a1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [3096, 10924], 'label': '31104.fx.5184.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.ct1', 'old_label': '5184.g1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247877
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.fv1', '1728.c1', '1728.k1', '1728.m1', '2592.s1', '2592.ca1', '2592.cq1'], 'contains': ['10368.h1', '15552.a1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [18144, 11764], 'label': '31104.fx.5184.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.bv1', 'old_label': '5184.h1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.h1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247878
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.fw1', '1728.c1', '1728.l1', '1728.m1', '2592.cq1'], 'contains': ['10368.h1', '15552.a1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [18216, 11764], 'label': '31104.fx.5184.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.bm1', 'old_label': '5184.i1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.i1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 186247879
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.w1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1728.n1', '1728.o1', '1728.p1', '2592.a1', '2592.cb1', '2592.ct1', '2592.cy1', '2592.db1', '2592.dc1', '2592.dd1', '2592.dg1', '2592.dj1', '2592.do1', '2592.dt1', '2592.dt2', '2592.dz1', '2592.eb1', '2592.ec1', '2592.ed1', '2592.ee1', '2592.ef1', '2592.eg1', '2592.ep1', '2592.ep2'], 'contains': ['10368.a1', '15552.b1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [16056, 22752], 'label': '31104.fx.5184.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '648.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '5184.j1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.j1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 186247880
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.d1', '36.f1', '36.k1'], 'contains': ['144.w1', '144.x1', '144.bc1', '144.dn1', '144.dt1', '144.ea1', '144.em1', '216.z1', '216.bf1', '216.bh1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [29077, 12096, 18576, 6, 22752, 18648, 10368], 'label': '31104.fx.72.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '72.k1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.k1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186247881
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.cm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1728.p1', '1728.q1', '1728.r1', '2592.b1', '2592.c1', '2592.cc1', '2592.cu1', '2592.dh1', '2592.dk1', '2592.dk2', '2592.dp1', '2592.du1', '2592.ea1', '2592.eh1', '2592.ei1', '2592.eq1'], 'contains': ['10368.b1', '15552.b1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [16056, 12384], 'label': '31104.fx.5184.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '5184.k1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.k1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247882
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.z1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1728.n1', '1728.q1', '2592.d1', '2592.cd1', '2592.cv1', '2592.cz1', '2592.de1', '2592.di1', '2592.dl1', '2592.dq1', '2592.dv1', '2592.dy1', '2592.ej1', '2592.el1', '2592.em1', '2592.eo1', '2592.er1'], 'contains': ['10368.c1', '15552.b1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [18576, 12096], 'label': '31104.fx.5184.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '5184.l1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.l1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247883
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.bs1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1728.n1', '1728.o1', '1728.r1', '2592.e1', '2592.g1', '2592.cf1', '2592.cw1', '2592.da1', '2592.df1', '2592.dm1', '2592.dm2', '2592.dr1', '2592.dw1', '2592.dw2', '2592.ek1', '2592.en1', '2592.er1', '2592.es1'], 'contains': ['10368.c1', '15552.b1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [2592, 12096], 'label': '31104.fx.5184.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.s1', 'old_label': '5184.m1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.m1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247884
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1728.o1', '1728.q1', '1728.r1', '2592.d1', '2592.f1', '2592.g1', '2592.ce1', '2592.cx1', '2592.dn1', '2592.dn2', '2592.dn3', '2592.ds1', '2592.dx1', '2592.es1'], 'contains': ['10368.c1', '15552.b1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [432, 12096], 'label': '31104.fx.5184.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1', 'old_label': '5184.n1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.n1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247885
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eq1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.ej1', '1728.s1', '1728.t1', '1728.w1', '1728.x1', '2592.h1', '2592.ey1'], 'contains': ['10368.d1', '15552.c1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [36, 12940], 'label': '31104.fx.5184.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ea1', 'old_label': '5184.o1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.o1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247886
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.gm1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.ek1', '1296.jv1', '1728.s1', '1728.u1', '1728.v1', '1728.y1', '2592.ew1', '2592.ex1', '2592.ez1'], 'contains': ['10368.e1', '15552.c1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [36, 16080], 'label': '31104.fx.5184.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.oi1', 'old_label': '5184.p1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.p1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247887
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54.bl1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1728.t1', '1728.u1', '1728.v1', '1728.z1', '1728.ba1', '2592.i1', '2592.ct1', '2592.fa1', '2592.fc1', '2592.fd1'], 'contains': ['10368.a1', '15552.c1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [36, 22752], 'label': '31104.fx.5184.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '576.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '5184.q1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.q1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247888
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.fk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1728.w1', '1728.x1', '1728.y1', '1728.ba1', '1728.bb1', '2592.j1', '2592.k1', '2592.cu1', '2592.fe1'], 'contains': ['10368.b1', '15552.c1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [36, 12384], 'label': '31104.fx.5184.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '576.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1', 'old_label': '5184.r1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.r1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247889
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1728.z1', '1728.bb1', '2592.l1', '2592.m1', '2592.cv1', '2592.cw1', '2592.cx1', '2592.fb1', '2592.ff1'], 'contains': ['10368.c1', '15552.c1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [36, 12096], 'label': '31104.fx.5184.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '576.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '5184.s1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.s1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247890
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.el1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1728.bc1', '1728.bd1', '1728.be1', '1728.bg1', '1728.bj1', '2592.cy1', '2592.fa1', '2592.fg1', '2592.fk1', '2592.fq1'], 'contains': ['10368.a1', '15552.d1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [12138, 22752], 'label': '31104.fx.5184.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.di1', 'old_label': '5184.t1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.t1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247891
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '9.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1'], 'contains': ['18.a1', '18.b1', '18.c1', '18.d1', '18.e1', '18.f1', '18.s1', '18.t1', '18.w1', '18.z1', '18.bm1', '27.d1', '27.e1'], 'core': '36.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [5713, 22752, 72, 2592, 10368, 6, 15552, 12096, 18576, 36], 'label': '31104.fx.9.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '9.d1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.d1', 'subgroup_fusion': None, 'weyl_group': '1728.39001'}
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id: 186247892
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1', '36.f1', '36.o1'], 'contains': ['144.w1', '144.bb1', '144.dr1', '144.du1', '144.ek1', '216.bi1', '216.bk1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [5713, 22752, 18576, 12138, 10368, 18648, 12096], 'label': '31104.fx.72.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '72.l1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.l1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186247893
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.le1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1728.bc1', '1728.bf1', '2592.cz1', '2592.da1', '2592.fb1', '2592.fh1', '2592.fl1', '2592.fl2', '2592.fm1'], 'contains': ['10368.c1', '15552.d1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [12138, 12096], 'label': '31104.fx.5184.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.gi1', 'old_label': '5184.u1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.u1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247894
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.go1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.kf1', '1728.bd1', '1728.bh1', '1728.bk1', '1728.bl1', '2592.ew1', '2592.fi1', '2592.fr1'], 'contains': ['10368.e1', '15552.d1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [14802, 20812], 'label': '31104.fx.5184.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.ok1', 'old_label': '5184.v1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.v1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247895
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.be1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.kg1', '1728.be1', '1728.bi1', '2592.fj1'], 'contains': ['10368.i1', '15552.d1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 1728, 'diagramx': None, 'generators': [17371, 29904], 'label': '31104.fx.5184.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '864.hg1', 'old_label': '5184.w1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.w1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247896
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.ev1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1728.bf1', '1728.bh1', '1728.bi1', '1728.bj1', '1728.bm1', '2592.db1', '2592.fc1', '2592.fo1', '2592.fp1', '2592.fq1'], 'contains': ['10368.a1', '15552.d1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [12138, 10368], 'label': '31104.fx.5184.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.x1', 'old_label': '5184.x1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.x1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247897
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.gr1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.ki1', '1728.bg1', '1728.bk1', '1728.bl1', '1728.bm1', '2592.ex1', '2592.fn1', '2592.fr1'], 'contains': ['10368.e1', '15552.d1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [17371, 23836], 'label': '31104.fx.5184.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fx1', 'old_label': '5184.y1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.y1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247898
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.ku1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1728.bn1', '1728.bo1', '1728.bp1', '1728.br1', '1728.bt1', '1728.bu1', '2592.dc1', '2592.fc1', '2592.fg1', '2592.fo1', '2592.fs1'], 'contains': ['10368.a1', '15552.e1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [6, 10368], 'label': '31104.fx.5184.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.gd1', 'old_label': '5184.z1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.z1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 186247899
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.gp1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.km1', '1728.bn1', '1728.bq1', '1728.bv1', '1728.bx1', '2592.ew1', '2592.fn1', '2592.ft1'], 'contains': ['10368.e1', '15552.e1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [26047, 5712], 'label': '31104.fx.5184.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.oj1', 'old_label': '5184.ba1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.ba1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247901
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.lh1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1728.bq1', '1728.bs1', '1728.bu1', '1728.ca1', '1728.cb1', '1728.cc1', '2592.dd1', '2592.fa1', '2592.fk1', '2592.fp1', '2592.fs1'], 'contains': ['10368.a1', '15552.e1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [6, 22752], 'label': '31104.fx.5184.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.dj1', 'old_label': '5184.bc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.bc1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247902
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.jt1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1728.bo1', '1728.ca1', '2592.de1', '2592.df1', '2592.fb1', '2592.fh1', '2592.fl1', '2592.fl2', '2592.fv1'], 'contains': ['10368.c1', '15552.e1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [6, 12096], 'label': '31104.fx.5184.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.gj1', 'old_label': '5184.bd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.bd1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247903
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.d1', '36.e1', '36.o1'], 'contains': ['144.w1', '144.be1', '144.ds1', '144.dv1', '144.en1', '216.bj1', '216.bl1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [8305, 22752, 18576, 12138, 10368, 18648, 12096], 'label': '31104.fx.72.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '72.m1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.m1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186247904
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.gq1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.kr1', '1728.bp1', '1728.bv1', '1728.by1', '1728.cb1', '2592.ex1', '2592.fi1', '2592.ft1'], 'contains': ['10368.e1', '15552.e1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [26047, 23836], 'label': '31104.fx.5184.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fx1', 'old_label': '5184.be1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.be1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247905
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.cb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.ks1', '1728.br1', '1728.bw1', '1728.bx1', '1728.bz1', '1728.cb1', '2592.fu1'], 'contains': ['10368.g1', '15552.e1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 576, 'diagramx': None, 'generators': [26047, 3100], 'label': '31104.fx.5184.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.dw1', 'old_label': '5184.bf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.bf1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247906
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.kt1', '1296.kt2', '1728.bt1', '1728.cc1', '2592.fj1'], 'contains': ['10368.i1', '15552.e1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 1728, 'diagramx': None, 'generators': [6, 19536], 'label': '31104.fx.5184.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '864.hg1', 'old_label': '5184.bg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.bg1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247907
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1728.cd1', '1728.ce1', '1728.cf1', '1728.cg1', '1728.ch1', '1728.ci1', '1728.cj1', '1728.cj2', '2592.n1', '2592.dg1', '2592.fd1', '2592.fg1', '2592.fp1', '2592.fw1', '2592.fy1'], 'contains': ['10368.a1', '15552.f1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [10405, 10368], 'label': '31104.fx.5184.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.d1', 'old_label': '5184.bh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.bh1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247908
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.di1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1728.cd1', '1728.ck1', '1728.cl1', '1728.cm1', '1728.cn1', '1728.co1', '1728.co2', '1728.cp1', '2592.o1', '2592.p1', '2592.dh1', '2592.fe1', '2592.fx1', '2592.fx2', '2592.fz1'], 'contains': ['10368.b1', '15552.f1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [10405, 12384], 'label': '31104.fx.5184.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.o1', 'old_label': '5184.bi1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.bi1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247909
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1728.ce1', '1728.ck1', '2592.q1', '2592.di1', '2592.ff1', '2592.fh1', '2592.gb1', '2592.gc1'], 'contains': ['10368.c1', '15552.f1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [10405, 1728], 'label': '31104.fx.5184.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.c1', 'old_label': '5184.bj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.bj1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247910
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.eu1', '1728.cf1', '1728.cl1', '1728.cm1', '1728.cq1', '2592.r1', '2592.ey1', '2592.ga1'], 'contains': ['10368.d1', '15552.f1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [10405, 12940], 'label': '31104.fx.5184.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.f1', 'old_label': '5184.bk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.bk1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247911
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ha1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.ev1', '1296.kz1', '1728.cg1', '1728.ch1', '1728.cn1', '1728.cq1', '2592.ez1', '2592.fi1', '2592.fn1'], 'contains': ['10368.e1', '15552.f1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [10405, 16080], 'label': '31104.fx.5184.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fz1', 'old_label': '5184.bl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.bl1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247912
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.ex1', '1728.ci1', '1728.co1', '1728.co2', '2592.s1'], 'contains': ['10368.h1', '15552.f1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [10405, 29404], 'label': '31104.fx.5184.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.h1', 'old_label': '5184.bm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.bm1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247913
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.bj1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.ey1', '1296.la1', '1728.cj1', '1728.cj2', '1728.cp1', '2592.fj1'], 'contains': ['10368.i1', '15552.f1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 576, 'diagramx': None, 'generators': [10405, 9168], 'label': '31104.fx.5184.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.dm1', 'old_label': '5184.bn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.bn1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247914
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1', '36.f1', '36.s1'], 'contains': ['144.x1', '144.bb1', '144.dz1', '144.ec1', '144.el1', '216.bm1', '216.bo1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [5713, 22752, 12096, 6, 10368, 18648, 18576], 'label': '31104.fx.72.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '72.n1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.n1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
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id: 186247915
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.ez1', '1728.cr1', '1728.cs1', '1728.ct1', '2592.h1', '2592.t1', '2592.ga1'], 'contains': ['10368.d1', '15552.g1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [3132, 12940], 'label': '31104.fx.5184.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.dz1', 'old_label': '5184.bo1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.bo1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247916
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.ea1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1728.cr1', '1728.cu1', '1728.cv1', '2592.i1', '2592.u1', '2592.z1', '2592.dj1', '2592.do1', '2592.fw1'], 'contains': ['10368.a1', '15552.g1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [18180, 10368], 'label': '31104.fx.5184.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.u1', 'old_label': '5184.bp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.bp1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247917
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.ea1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1728.cs1', '1728.cv1', '1728.cw3', '2592.k1', '2592.v1', '2592.bb1', '2592.dk2', '2592.dp1', '2592.fx1'], 'contains': ['10368.b1', '15552.g1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [18180, 12384], 'label': '31104.fx.5184.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '5184.bq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.bq1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247918
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.bq2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.ea1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1728.ct1', '1728.cv1', '1728.cw1', '1728.cw2', '2592.j1', '2592.w1', '2592.ba1', '2592.dk1', '2592.dp1', '2592.fx2'], 'contains': ['10368.b1', '15552.g1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [3132, 12384], 'label': '31104.fx.5184.bq2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.y1', 'old_label': '5184.bq2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.bq2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247919
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1728.cu1', '1728.cw1', '1728.cw3', '2592.l1', '2592.x2', '2592.y2', '2592.bd1', '2592.dm1', '2592.dn3', '2592.dq1', '2592.ds1', '2592.gb1'], 'contains': ['10368.c1', '15552.g1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [18684, 12096], 'label': '31104.fx.5184.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '5184.br1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.br1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 186247920
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.br2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1728.cu1', '1728.cw2', '1728.cw3', '2592.m1', '2592.x1', '2592.y1', '2592.bc1', '2592.bd1', '2592.dl1', '2592.dm2', '2592.dn1', '2592.dn2', '2592.dr1', '2592.ds1'], 'contains': ['10368.c1', '15552.g1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [15588, 12096], 'label': '31104.fx.5184.br2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.di1', 'old_label': '5184.br2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.br2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247921
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.i1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1728.cx1', '1728.cx2', '1728.cy1', '2592.u1', '2592.be1', '2592.ct1', '2592.dj1', '2592.dt1', '2592.dt2', '2592.fk1', '2592.fo1', '2592.fy1'], 'contains': ['10368.a1', '15552.h1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [16092, 22752], 'label': '31104.fx.5184.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '5184.bs1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.bs1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247922
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.bd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1728.cy1', '1728.cz1', '1728.cz2', '2592.v1', '2592.w1', '2592.bf1', '2592.bg1', '2592.cu1', '2592.dk1', '2592.dk2', '2592.du1', '2592.fz1'], 'contains': ['10368.b1', '15552.h1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [16092, 12384], 'label': '31104.fx.5184.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.w1', 'old_label': '5184.bt1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.bt1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247923
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1728.cx1', '1728.cx2', '1728.cz2', '2592.y1', '2592.bh1', '2592.bi1', '2592.cw1', '2592.dm1', '2592.dn1', '2592.dv1', '2592.dw2', '2592.dx1', '2592.fl2'], 'contains': ['10368.c1', '15552.h1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [2628, 12096], 'label': '31104.fx.5184.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.t1', 'old_label': '5184.bu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.bu1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247924
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.bu2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1728.cx1', '1728.cz1', '1728.cz2', '2592.x1', '2592.y2', '2592.bh2', '2592.bi1', '2592.bi2', '2592.cx1', '2592.dl1', '2592.dm2', '2592.dn3', '2592.dw1', '2592.dx1'], 'contains': ['10368.c1', '15552.h1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [540, 12096], 'label': '31104.fx.5184.bu2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.di1', 'old_label': '5184.bu2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.bu2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247925
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.d1', '36.e1', '36.s1'], 'contains': ['144.x1', '144.be1', '144.eb1', '144.ed1', '144.eo1', '216.bn1', '216.bp1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [8305, 22752, 12096, 6, 10368, 18648, 18576], 'label': '31104.fx.72.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '72.o1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.o1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
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id: 186247926
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.bu3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1728.cx2', '1728.cz1', '2592.x2', '2592.bi2', '2592.cv1', '2592.dn2', '2592.dw2', '2592.fl1', '2592.gc1'], 'contains': ['10368.c1', '15552.h1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [18612, 12096], 'label': '31104.fx.5184.bu3', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '5184.bu3', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.bu3', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247927
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1728.da1', '1728.db1', '2592.bj1', '2592.dy1', '2592.ff1', '2592.fm1', '2592.fv1', '2592.gb1', '2592.gc1'], 'contains': ['10368.c1', '15552.i1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1, 1728], 'label': '31104.fx.5184.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.a1', 'old_label': '5184.bv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.bv1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247928
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.z1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1728.da1', '1728.dc1', '1728.dd1', '1728.de1', '1728.df1', '1728.dg1', '2592.bk1', '2592.dz1', '2592.fd1', '2592.fq1', '2592.fs1', '2592.fw1', '2592.fy1'], 'contains': ['10368.a1', '15552.i1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1, 22752], 'label': '31104.fx.5184.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '5184.bw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.bw1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247929
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.dc1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1728.db1', '1728.dg1', '1728.dh1', '1728.di1', '1728.dj1', '1728.dk1', '2592.bl1', '2592.bm1', '2592.ea1', '2592.fe1', '2592.fx1', '2592.fx2', '2592.fz1'], 'contains': ['10368.b1', '15552.i1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1, 12384], 'label': '31104.fx.5184.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.q1', 'old_label': '5184.bx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.bx1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247930
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.fj1', '1728.dc1', '1728.dh1', '1728.di1', '1728.dl1', '1728.dm1', '1728.dn1', '1728.do1', '2592.bn1', '2592.ey1', '2592.ga1'], 'contains': ['10368.d1', '15552.i1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [1, 556], 'label': '31104.fx.5184.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1296.bd1', 'old_label': '5184.by1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.by1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247931
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.fk1', '1296.li1', '1728.dd1', '1728.de1', '1728.dj1', '1728.dl1', '1728.dn1', '1728.dp1', '1728.dq1', '2592.ez1', '2592.fr1', '2592.ft1'], 'contains': ['10368.e1', '15552.i1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 2592, 'diagramx': None, 'generators': [1, 5712], 'label': '31104.fx.5184.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1296.lr1', 'old_label': '5184.bz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.bz1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247932
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.fm1', '1728.dc1', '1728.dh1', '1728.dk1', '1728.dl1', '1728.dm1', '1728.dp1', '1728.dq1', '1728.dr1', '1728.dr2', '2592.bo1'], 'contains': ['10368.f1', '15552.i1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 2592, 'diagramx': None, 'generators': [1, 10924], 'label': '31104.fx.5184.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2592.bo1', 'old_label': '5184.ca1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.ca1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247933
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '5184.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.fn1', '1296.lj1', '1728.dd1', '1728.df1', '1728.dj1', '1728.dl1', '1728.dm1', '1728.do1', '1728.dp1', '1728.dr1', '1728.dr2', '2592.fu1'], 'contains': ['10368.g1', '15552.i1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 5184, 'diagramx': None, 'generators': [1, 28464], 'label': '31104.fx.5184.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2592.fu1', 'old_label': '5184.cb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.cb1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247934
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '7776.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.a1', '2592.b1', '2592.c1', '2592.d1', '2592.e1', '2592.f1', '2592.g1', '3888.a1', '3888.b1', '3888.c1', '3888.d1', '3888.e1', '3888.y1', '3888.bd1'], 'contains': ['15552.a1', '15552.b1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [16056, 15552], 'label': '31104.fx.7776.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1944.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '7776.a1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 186247935
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '7776.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.h1', '2592.i1', '2592.j1', '2592.k1', '2592.l1', '2592.m1', '3888.a1', '3888.f1', '3888.g1', '3888.n1', '3888.z1'], 'contains': ['15552.a1', '15552.c1', '15552.g1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [36, 18144], 'label': '31104.fx.7776.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.q1', 'old_label': '7776.b1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 186247936
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.t1', '36.bc1', '36.bf1'], 'contains': ['144.n1', '144.o1', '144.y1', '144.z1', '144.bf1', '216.bq1', '216.bs1', '216.bt1', '216.bt2'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [16057, 22752, 12096, 16092, 10368, 2592, 15552], 'label': '31104.fx.72.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '72.p1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.p1', 'subgroup_fusion': None, 'weyl_group': '432.768'}
-
id: 186247937
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '7776.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.n1', '2592.o1', '2592.p1', '2592.q1', '2592.r1', '2592.s1', '3888.b1', '3888.f1', '3888.h1', '3888.i1', '3888.j1', '3888.q1', '3888.ba1'], 'contains': ['15552.a1', '15552.f1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [10405, 18144], 'label': '31104.fx.7776.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cr1', 'old_label': '7776.c1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 186247938
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '7776.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.u1', '2592.v1', '2592.w1', '2592.x1', '2592.x2', '2592.y1', '2592.y2', '3888.c1', '3888.d1', '3888.h1', '3888.k1', '3888.n1', '3888.r1', '3888.bb1'], 'contains': ['15552.a1', '15552.g1', '15552.h1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [3132, 18144], 'label': '31104.fx.7776.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.h1', 'old_label': '7776.d1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 186247939
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '7776.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.de1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.t1', '2592.z1', '2592.ba1', '2592.bb1', '2592.bc1', '2592.bd1', '3888.d1', '3888.i1', '3888.l1', '3888.r1', '3888.z1'], 'contains': ['15552.a1', '15552.g1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [108, 18144], 'label': '31104.fx.7776.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.q1', 'old_label': '7776.e1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247940
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '7776.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.be1', '2592.bf1', '2592.bg1', '2592.bh1', '2592.bh2', '2592.bi1', '2592.bi2', '3888.a1', '3888.c1', '3888.j1', '3888.m1', '3888.r1', '3888.s1', '3888.bb1'], 'contains': ['15552.a1', '15552.h1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [18612, 18144], 'label': '31104.fx.7776.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.h1', 'old_label': '7776.f1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247941
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '7776.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.bj1', '2592.bk1', '2592.bl1', '2592.bm1', '2592.bn1', '2592.bo1', '3888.e1', '3888.f1', '3888.h1', '3888.l1', '3888.m1', '3888.t1', '3888.bc1'], 'contains': ['15552.a1', '15552.i1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1, 18144], 'label': '31104.fx.7776.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cp1', 'old_label': '7776.g1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247942
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '7776.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.bp1', '2592.br1', '2592.bs1', '2592.bv1', '2592.bx1', '2592.ca1', '3888.b1', '3888.g1', '3888.k1', '3888.l1', '3888.m1', '3888.v1', '3888.ba1'], 'contains': ['15552.a1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26029], 'label': '31104.fx.7776.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cr1', 'old_label': '7776.h1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.h1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247943
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '7776.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.w1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.bq1', '2592.bt1', '2592.bu1', '2592.bw1', '2592.by1', '2592.bz1', '3888.e1', '3888.g1', '3888.i1', '3888.j1', '3888.k1', '3888.x1', '3888.bc1'], 'contains': ['15552.a1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [15625], 'label': '31104.fx.7776.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cp1', 'old_label': '7776.i1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.i1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247944
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '7776.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.cb1', '2592.cc1', '2592.cd1', '2592.ce1', '2592.cf1', '3888.n1', '3888.o1', '3888.p1', '3888.q1', '3888.r1', '3888.s1', '3888.t1', '3888.u1', '3888.v1', '3888.w1', '3888.x1', '3888.y1', '3888.bd1'], 'contains': ['15552.a1', '15552.b1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [18144, 16056], 'label': '31104.fx.7776.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1944.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '7776.j1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.j1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247945
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '7776.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.cg1', '2592.ch1', '2592.ci1', '2592.cj1', '2592.ck1', '2592.cl1', '2592.cm1', '2592.cn1', '2592.co1', '2592.cp1', '2592.cq1', '2592.cr1', '2592.cs1', '3888.z1', '3888.ba1', '3888.bb1', '3888.bc1', '3888.bd1'], 'contains': ['15552.a1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [3096, 15552], 'label': '31104.fx.7776.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1944.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '7776.k1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.k1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247946
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '7776.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '243.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.ct1', '2592.cu1', '2592.cv1', '2592.cw1', '2592.cx1', '3888.a1', '3888.n1', '3888.be1', '3888.bf1', '3888.bg1', '3888.bh1', '3888.cm1'], 'contains': ['15552.b1', '15552.c1', '15552.h1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [36, 16056], 'label': '31104.fx.7776.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '7776.l1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.l1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 186247947
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.e1', '36.h1', '36.bf1'], 'contains': ['144.y1', '144.ba1', '144.be1', '144.ef1', '216.br1', '216.bu1', '216.bv1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [433, 22752, 12096, 468, 10368, 15552, 2592], 'label': '31104.fx.72.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '72.q1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.q1', 'subgroup_fusion': None, 'weyl_group': '864.4406'}
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id: 186247948
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '7776.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.gi1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2592.cy1', '2592.cz1', '2592.da1', '2592.db1', '3888.o1', '3888.be1', '3888.bi1', '3888.bj1', '3888.bk1', '3888.bl1', '3888.bm1', '3888.bn1', '3888.bo1', '3888.bp1', '3888.bq1', '3888.br1', '3888.bs1', '3888.cn1', '3888.co1'], 'contains': ['15552.b1', '15552.d1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [17371, 18576], 'label': '31104.fx.7776.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '7776.m1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.m1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247949
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '7776.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.er1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2592.dc1', '2592.dd1', '2592.de1', '2592.df1', '3888.p1', '3888.be1', '3888.bi1', '3888.bj1', '3888.bk1', '3888.bt1', '3888.bu1', '3888.bv1', '3888.bw1', '3888.bx1', '3888.by1', '3888.bz1', '3888.ca1', '3888.cp1', '3888.cq1'], 'contains': ['15552.b1', '15552.e1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [6, 16056], 'label': '31104.fx.7776.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '7776.n1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.n1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247950
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '7776.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.dg1', '2592.dh1', '2592.di1', '3888.q1', '3888.bf1', '3888.bi1', '3888.bl1', '3888.bt1', '3888.cb1', '3888.cc1', '3888.cd1', '3888.cr1'], 'contains': ['15552.b1', '15552.f1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [10405, 2592], 'label': '31104.fx.7776.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '7776.o1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.o1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247951
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '7776.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.dj1', '2592.dk1', '2592.dk2', '2592.dl1', '2592.dm1', '2592.dm2', '2592.dn1', '2592.dn2', '2592.dn3', '3888.a1', '3888.c1', '3888.d1', '3888.r1', '3888.cs1'], 'contains': ['15552.b1', '15552.g1', '15552.h1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [15588, 16056], 'label': '31104.fx.7776.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.ba1', 'old_label': '7776.p1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.p1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 186247952
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '7776.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.do1', '2592.dp1', '2592.dq1', '2592.dr1', '2592.ds1', '3888.d1', '3888.n1', '3888.bm1', '3888.bu1', '3888.cb1', '3888.ce1', '3888.cs1'], 'contains': ['15552.b1', '15552.g1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [18180, 16056], 'label': '31104.fx.7776.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '7776.q1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.q1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247953
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '7776.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2592.dt1', '2592.dt2', '2592.du1', '2592.dv1', '2592.dw1', '2592.dw2', '2592.dx1', '3888.c1', '3888.s1', '3888.bj1', '3888.bn1', '3888.bv1', '3888.cc1', '3888.cf1', '3888.cg1', '3888.cm1', '3888.cs1'], 'contains': ['15552.b1', '15552.h1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [468, 16056], 'label': '31104.fx.7776.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '7776.r1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.r1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247954
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '7776.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.dy1', '2592.dz1', '2592.ea1', '3888.t1', '3888.bf1', '3888.bo1', '3888.br1', '3888.bw1', '3888.bz1', '3888.cb1', '3888.cf1', '3888.ch1', '3888.ci1', '3888.ct1'], 'contains': ['15552.b1', '15552.i1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1, 2592], 'label': '31104.fx.7776.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '7776.s1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.s1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247955
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '7776.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.gh1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2592.eb1', '2592.ec1', '2592.ej1', '2592.ek1', '3888.o1', '3888.bg1', '3888.bo1', '3888.bp1', '3888.bt1', '3888.bu1', '3888.bv1', '3888.bx1', '3888.cd1', '3888.cg1', '3888.ch1', '3888.cj1', '3888.ck1', '3888.cn1', '3888.cu1'], 'contains': ['15552.b1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [30282], 'label': '31104.fx.7776.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '7776.t1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.t1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247956
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '7776.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.ed1', '2592.eh1', '2592.el1', '3888.u1', '3888.bh1', '3888.bk1', '3888.bq1', '3888.bx1', '3888.ce1', '3888.cf1', '3888.cj1', '3888.cr1'], 'contains': ['15552.b1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [26389], 'label': '31104.fx.7776.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '7776.u1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.u1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 186247957
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '7776.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.em1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2592.ee1', '2592.ef1', '2592.em1', '2592.en1', '3888.p1', '3888.bg1', '3888.bl1', '3888.bm1', '3888.bn1', '3888.bq1', '3888.bw1', '3888.by1', '3888.cd1', '3888.cg1', '3888.ci1', '3888.cj1', '3888.cl1', '3888.cp1', '3888.cv1'], 'contains': ['15552.b1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [18150], 'label': '31104.fx.7776.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '7776.v1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.v1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247958
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.v1', '36.bc1', '36.bj1'], 'contains': ['144.t1', '144.u1', '144.z1', '144.bb1', '144.bd1', '216.bw1', '216.bx1', '216.by1', '216.bz1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1, 22752, 12096, 16092, 10368, 2592, 15552], 'label': '31104.fx.72.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '72.r1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.r1', 'subgroup_fusion': None, 'weyl_group': '432.768'}
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id: 186247959
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '7776.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.eg1', '2592.ei1', '2592.eo1', '3888.w1', '3888.bh1', '3888.bp1', '3888.bs1', '3888.by1', '3888.ca1', '3888.cc1', '3888.ce1', '3888.ck1', '3888.cl1', '3888.ct1'], 'contains': ['15552.b1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [15985], 'label': '31104.fx.7776.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '7776.w1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.w1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247960
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '7776.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2592.ep1', '2592.ep2', '2592.eq1', '2592.er1', '2592.es1', '2592.et1', '2592.eu1', '2592.ev1', '2592.ev2', '3888.y1', '3888.cm1', '3888.cn1', '3888.co1', '3888.cp1', '3888.cq1', '3888.cr1', '3888.cs1', '3888.ct1', '3888.cu1', '3888.cv1'], 'contains': ['15552.b1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [16056, 18576], 'label': '31104.fx.7776.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1944.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '7776.x1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.x1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 186247961
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '7776.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.el1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2592.ew1', '2592.ex1', '2592.fa1', '2592.fb1', '2592.fc1', '3888.be1', '3888.cw1'], 'contains': ['15552.c1', '15552.d1', '15552.e1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [24198, 36], 'label': '31104.fx.7776.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.el1', 'old_label': '7776.y1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.y1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 186247962
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '7776.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.ey1', '2592.ez1', '2592.fd1', '2592.fe1', '2592.ff1', '3888.f1', '3888.bf1', '3888.cw1'], 'contains': ['15552.c1', '15552.f1', '15552.i1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [20737, 36], 'label': '31104.fx.7776.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.a1', 'old_label': '7776.z1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.z1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 186247963
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '7776.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.gl1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2592.fg1', '2592.fh1', '2592.fi1', '2592.fj1', '2592.fn1', '2592.fp1', '3888.bi1', '3888.cw1', '3888.cx1'], 'contains': ['15552.d1', '15552.e1', '15552.f1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [26485, 12138], 'label': '31104.fx.7776.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.gl1', 'old_label': '7776.ba1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.ba1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 186247964
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '7776.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.bg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2592.fk1', '2592.fl1', '2592.fl2', '2592.fo1', '3888.be1', '3888.bj1', '3888.cx1'], 'contains': ['15552.d1', '15552.e1', '15552.h1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': None, 'generators': [24198, 16092], 'label': '31104.fx.7776.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.bg1', 'old_label': '7776.bb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.bb1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 186247965
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '7776.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.gh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.fm1', '2592.fq1', '2592.fr1', '3888.br1', '3888.cw1', '3888.cx1'], 'contains': ['15552.d1', '15552.i1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [5713, 12138], 'label': '31104.fx.7776.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.gh1', 'old_label': '7776.bc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.bc1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 186247966
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '7776.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.bp1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.fs1', '2592.ft1', '2592.fu1', '2592.fv1', '3888.bz1', '3888.cw1', '3888.cx1'], 'contains': ['15552.e1', '15552.i1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': None, 'generators': [5713, 6], 'label': '31104.fx.7776.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1944.bp1', 'old_label': '7776.bd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.bd1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 186247967
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '7776.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.fw1', '2592.fx1', '2592.fx2', '2592.ga1', '2592.gb1', '3888.f1', '3888.h1', '3888.cb1'], 'contains': ['15552.f1', '15552.g1', '15552.i1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': None, 'generators': [20737, 18180], 'label': '31104.fx.7776.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1944.e1', 'old_label': '7776.be1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.be1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 186247968
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '7776.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.fy1', '2592.fz1', '2592.gc1', '3888.h1', '3888.bf1', '3888.cx1'], 'contains': ['15552.f1', '15552.h1', '15552.i1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [20737, 2628], 'label': '31104.fx.7776.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.a1', 'old_label': '7776.bf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.bf1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 186247969
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.t1', '36.bd1', '36.bj1'], 'contains': ['144.z1', '144.bc1', '144.bf1', '216.ca1', '216.cc1', '216.ce1', '216.ce2'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [15625, 22752, 12096, 16092, 10368, 18144, 2592], 'label': '31104.fx.72.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '72.s1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.s1', 'subgroup_fusion': None, 'weyl_group': '432.768'}
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id: 186247970
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '10368.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.c1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['3456.a1', '3456.b1', '3456.c1', '3456.d1', '3456.e1', '3456.f1', '3456.g1', '3456.h1', '3456.h2', '5184.a1', '5184.j1', '5184.q1', '5184.t1', '5184.x1', '5184.z1', '5184.bc1', '5184.bh1', '5184.bp1', '5184.bs1', '5184.bw1'], 'contains': ['31104.a1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [10368], 'label': '31104.fx.10368.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '10368.a1', 'normal_contained_in': ['648.a1', '3456.a1'], 'normal_contains': ['31104.a1'], 'normalizer': '1.a1', 'old_label': '10368.a1', 'projective_image': '31104.fx', 'quotient_action_image': '2.1', 'quotient_action_kernel': '5184.ov', 'quotient_action_kernel_order': 5184, 'quotient_fusion': None, 'short_label': '10368.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247971
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '10368.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3456.a1', '3456.i1', '3456.j1', '3456.k1', '3456.l1', '3456.m1', '3456.n1', '3456.n2', '3456.o1', '5184.b1', '5184.c1', '5184.k1', '5184.r1', '5184.bi1', '5184.bq1', '5184.bq2', '5184.bt1', '5184.bx1'], 'contains': ['31104.a1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [12384], 'label': '31104.fx.10368.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '3456.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '10368.b1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10368.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 186247972
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '10368.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.z1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3456.b1', '3456.i1', '5184.d1', '5184.e1', '5184.l1', '5184.m1', '5184.n1', '5184.s1', '5184.u1', '5184.bd1', '5184.bj1', '5184.br1', '5184.br2', '5184.bu1', '5184.bu2', '5184.bu3', '5184.bv1'], 'contains': ['31104.a1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [12096], 'label': '31104.fx.10368.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1152.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '10368.c1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10368.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247973
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '10368.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.cl1', '3456.c1', '3456.j1', '3456.k1', '3456.p1', '3456.q1', '3456.r1', '3456.s1', '5184.f1', '5184.o1', '5184.bk1', '5184.bo1', '5184.by1'], 'contains': ['31104.a1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [24460], 'label': '31104.fx.10368.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1', 'old_label': '10368.d1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10368.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 186247974
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '10368.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2592.cm1', '2592.et1', '3456.d1', '3456.e1', '3456.l1', '3456.p1', '3456.r1', '3456.t1', '3456.u1', '5184.p1', '5184.v1', '5184.y1', '5184.ba1', '5184.be1', '5184.bl1', '5184.bz1'], 'contains': ['31104.a1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [20812], 'label': '31104.fx.10368.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bc1', 'old_label': '10368.e1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10368.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 186247975
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '10368.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.co1', '3456.c1', '3456.j1', '3456.m1', '3456.p1', '3456.q1', '3456.t1', '3456.u1', '3456.v1', '3456.v2', '5184.g1', '5184.ca1'], 'contains': ['31104.a1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [10924], 'label': '31104.fx.10368.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.t1', 'old_label': '10368.f1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10368.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 186247976
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '10368.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2592.cp1', '2592.eu1', '3456.d1', '3456.f1', '3456.l1', '3456.p1', '3456.q1', '3456.s1', '3456.t1', '3456.v1', '3456.v2', '5184.bb1', '5184.bf1', '5184.cb1'], 'contains': ['31104.a1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [28464], 'label': '31104.fx.10368.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.ba1', 'old_label': '10368.g1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10368.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247977
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '10368.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.cr1', '3456.g1', '3456.n1', '3456.n2', '5184.h1', '5184.i1', '5184.bm1'], 'contains': ['31104.a1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [11764], 'label': '31104.fx.10368.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.bv1', 'old_label': '10368.h1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10368.h1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247978
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '10368.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2592.cs1', '2592.ev1', '2592.ev2', '3456.h1', '3456.h2', '3456.o1', '5184.w1', '5184.bg1', '5184.bn1'], 'contains': ['31104.a1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 576, 'diagramx': None, 'generators': [29904], 'label': '31104.fx.10368.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.dm1', 'old_label': '10368.i1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10368.i1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 186247979
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '15552.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5184.a1', '5184.b1', '5184.c1', '5184.d1', '5184.e1', '5184.f1', '5184.g1', '5184.h1', '5184.i1', '7776.a1', '7776.b1', '7776.c1', '7776.d1', '7776.e1', '7776.f1', '7776.g1', '7776.h1', '7776.i1', '7776.j1', '7776.k1'], 'contains': ['31104.a1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [18144], 'label': '31104.fx.15552.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1944.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '15552.a1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15552.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 186247980
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.v1', '36.bd1', '36.bf1'], 'contains': ['144.z1', '144.bd1', '144.be1', '216.cb1', '216.cd1', '216.cf1', '216.cg1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [433, 22752, 12096, 16092, 10368, 15552, 2592], 'label': '31104.fx.72.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '72.t1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.t1', 'subgroup_fusion': None, 'weyl_group': '432.768'}
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id: 186247981
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '15552.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5184.j1', '5184.k1', '5184.l1', '5184.m1', '5184.n1', '7776.a1', '7776.j1', '7776.l1', '7776.m1', '7776.n1', '7776.o1', '7776.p1', '7776.q1', '7776.r1', '7776.s1', '7776.t1', '7776.u1', '7776.v1', '7776.w1', '7776.x1'], 'contains': ['31104.a1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [16056], 'label': '31104.fx.15552.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1944.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '15552.b1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15552.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 186247982
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '15552.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '27.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5184.o1', '5184.p1', '5184.q1', '5184.r1', '5184.s1', '7776.b1', '7776.l1', '7776.y1', '7776.z1'], 'contains': ['31104.a1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [36], 'label': '31104.fx.15552.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '576.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '15552.c1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15552.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 186247983
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '15552.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.di1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['5184.t1', '5184.u1', '5184.v1', '5184.w1', '5184.x1', '5184.y1', '7776.m1', '7776.y1', '7776.ba1', '7776.bb1', '7776.bc1'], 'contains': ['31104.a1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [12138], 'label': '31104.fx.15552.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.di1', 'old_label': '15552.d1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15552.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 186247984
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '15552.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.gd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['5184.z1', '5184.ba1', '5184.bb1', '5184.bc1', '5184.bd1', '5184.be1', '5184.bf1', '5184.bg1', '7776.n1', '7776.y1', '7776.ba1', '7776.bb1', '7776.bd1'], 'contains': ['31104.a1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [26047], 'label': '31104.fx.15552.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.gd1', 'old_label': '15552.e1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15552.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 186247985
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '15552.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5184.bh1', '5184.bi1', '5184.bj1', '5184.bk1', '5184.bl1', '5184.bm1', '5184.bn1', '7776.c1', '7776.o1', '7776.z1', '7776.ba1', '7776.be1', '7776.bf1'], 'contains': ['31104.a1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [10405], 'label': '31104.fx.15552.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.d1', 'old_label': '15552.f1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15552.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 186247986
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '15552.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5184.bo1', '5184.bp1', '5184.bq1', '5184.bq2', '5184.br1', '5184.br2', '7776.b1', '7776.d1', '7776.e1', '7776.p1', '7776.q1', '7776.be1'], 'contains': ['31104.a1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [18180], 'label': '31104.fx.15552.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.q1', 'old_label': '15552.g1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15552.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 186247987
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '15552.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '243.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5184.bs1', '5184.bt1', '5184.bu1', '5184.bu2', '5184.bu3', '7776.d1', '7776.f1', '7776.l1', '7776.p1', '7776.r1', '7776.bb1', '7776.bf1'], 'contains': ['31104.a1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [16092], 'label': '31104.fx.15552.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '15552.h1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15552.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 186247988
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '15552.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5184.bv1', '5184.bw1', '5184.bx1', '5184.by1', '5184.bz1', '5184.ca1', '5184.cb1', '7776.g1', '7776.s1', '7776.z1', '7776.bc1', '7776.bd1', '7776.be1', '7776.bf1'], 'contains': ['31104.a1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1], 'label': '31104.fx.15552.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.a1', 'old_label': '15552.i1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15552.i1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 186247989
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '31104.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': ['1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['10368.a1', '10368.b1', '10368.c1', '10368.d1', '10368.e1', '10368.f1', '10368.g1', '10368.h1', '10368.i1', '15552.a1', '15552.b1', '15552.c1', '15552.d1', '15552.e1', '15552.f1', '15552.g1', '15552.h1', '15552.i1'], 'contains': [], 'core': '31104.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [], 'label': '31104.fx.31104.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '31104.a1', 'normal_contained_in': ['1944.a1', '10368.a1'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '31104.a1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '31104.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 186247990
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.f1', '36.h1', '36.bj1'], 'contains': ['144.ba1', '144.bb1', '144.bc1', '144.ei1', '216.ch1', '216.ci1', '216.cj1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1, 22752, 12096, 468, 10368, 18144, 2592], 'label': '31104.fx.72.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '72.u1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.u1', 'subgroup_fusion': None, 'weyl_group': '864.4406'}
-
id: 186247991
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '12.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': ['2592.fu1', '2592.ft1', '2592.fn1', '2592.fr1', '2592.fi1', '2592.fj1'], 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '6.a1', '6.e1', '6.g1'], 'contains': ['24.a1', '36.a1', '36.bm1', '36.bo1', '48.h1', '48.v1'], 'core': '12.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [36, 10368, 2592, 15552, 5712, 432, 22752, 12096, 15624], 'label': '31104.fx.12.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': ['4.a1', '6.a1'], 'normal_contains': ['24.a1', '36.a1'], 'normalizer': '1.a1', 'old_label': '12.a1', 'projective_image': '31104.fx', 'quotient_action_image': '12.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.a1', 'subgroup_fusion': None, 'weyl_group': '31104.fx'}
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id: 186247992
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.j1', '36.bf1', '36.bj1'], 'contains': ['144.ba1', '144.bd1', '144.bf1', '216.ck1', '216.cl1', '216.cm1', '216.cn1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [16057, 22752, 12096, 468, 10368, 15552, 2592], 'label': '31104.fx.72.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '72.v1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.v1', 'subgroup_fusion': None, 'weyl_group': '432.768'}
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id: 186247993
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1', '36.g1', '36.h1', '36.i1', '36.j1'], 'contains': ['144.a1', '144.c1', '144.v1', '144.ba1', '144.bg1', '144.es1', '144.fq1', '216.co1', '216.cp1', '216.cq1', '216.cr1', '216.cs1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [36, 22752, 12096, 18576, 10368, 18144, 16056], 'label': '31104.fx.72.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '72.w1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.w1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
-
id: 186247994
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.gc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.g1', '36.k1', '36.l1', '36.m1', '36.n1', '36.o1', '36.bs1'], 'contains': ['144.w1', '144.bg1', '144.eu1', '144.ev1', '144.fv1', '216.ct1', '216.cu1', '216.cv1', '216.cw1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [17371, 18576, 10368, 16056, 22752, 2592, 12096], 'label': '31104.fx.72.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '72.x1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.x1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
-
id: 186247995
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ep1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.g1', '36.k1', '36.p1', '36.q1', '36.r1', '36.s1', '36.cj1'], 'contains': ['144.x1', '144.bg1', '144.fg1', '144.fl1', '144.fw1', '216.cx1', '216.cy1', '216.cz1', '216.da1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [26047, 12096, 18576, 16056, 10368, 2592, 22752], 'label': '31104.fx.72.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '72.y1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.y1', 'subgroup_fusion': None, 'weyl_group': '288.977'}
-
id: 186247996
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.h1', '36.k1', '36.t1', '36.u1', '36.cm1'], 'contains': ['144.y1', '144.bc1', '144.bg1', '144.fm1', '216.db1', '216.dc1', '216.dd1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [10405, 2592, 10368, 18576, 1728, 18144, 22752], 'label': '31104.fx.72.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '72.z1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.z1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186247997
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1', '36.l1', '36.p1', '36.t1', '36.v1'], 'contains': ['144.c1', '144.d1', '144.z1', '144.bg1', '144.fq1', '216.de1', '216.df1', '216.dg1', '216.dh1', '216.di1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [15588, 22752, 12096, 18576, 10368, 18144, 16056], 'label': '31104.fx.72.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '72.ba1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ba1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
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id: 186247998
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.h1', '36.o1', '36.s1', '36.v1', '36.w1', '36.x1', '36.cz1'], 'contains': ['144.bb1', '144.be1', '144.bg1', '144.ft1', '216.dj1', '216.dk1', '216.dl1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1, 22752, 2592, 18576, 10368, 18144, 12096], 'label': '31104.fx.72.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '72.bb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bb1', 'subgroup_fusion': None, 'weyl_group': '288.977'}
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id: 186247999
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.gc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.i1', '36.n1', '36.p1', '36.q1', '36.u1', '36.w1', '36.bs1'], 'contains': ['144.bg1', '144.fv1', '216.dm1', '216.dn1', '216.do1', '216.du1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1819, 18576, 2592, 16056, 22752, 12096, 10368], 'label': '31104.fx.72.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '72.bc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bc1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186248000
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.j1', '36.m1', '36.q1', '36.v1', '36.cm1'], 'contains': ['144.bd1', '144.bg1', '216.dp1', '216.dv1', '216.dy1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [26461, 2592, 15552, 18576, 1728, 22752, 10368], 'label': '31104.fx.72.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '72.bd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bd1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186248001
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ep1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.i1', '36.l1', '36.m1', '36.r1', '36.u1', '36.x1', '36.cj1'], 'contains': ['144.bg1', '144.fw1', '216.dq1', '216.dr1', '216.ds1', '216.dw1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [10495, 12096, 18576, 16056, 10368, 22752, 2592], 'label': '31104.fx.72.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '72.be1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.be1', 'subgroup_fusion': None, 'weyl_group': '288.977'}
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id: 186248002
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '12.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': ['2592.ex1', '2592.ez1', '2592.ey1', '2592.ga1', '2592.ft1', '2592.fu1', '2592.fn1'], 'conjugacy_class_count': 2, 'contained_in': ['4.b1', '6.a1', '6.i1', '6.l1'], 'contains': ['24.a1', '36.b1', '36.bs1', '36.bv1', '48.x1'], 'core': '12.b1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [17371, 15552, 22752, 16056, 12096, 23836, 2592, 18576, 10368], 'label': '31104.fx.12.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': ['4.b1', '6.a1'], 'normal_contains': ['24.a1', '36.b1'], 'normalizer': '1.a1', 'old_label': '12.b1', 'projective_image': '31104.fx', 'quotient_action_image': '12.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.b1', 'subgroup_fusion': None, 'weyl_group': '10368.pi'}
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id: 186248003
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.j1', '36.n1', '36.r1', '36.t1', '36.cz1'], 'contains': ['144.bf1', '144.bg1', '216.dt1', '216.dx1', '216.dz1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [16057, 22752, 2592, 18576, 10368, 12096, 15552], 'label': '31104.fx.72.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '72.bf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bf1', 'subgroup_fusion': None, 'weyl_group': '288.977'}
-
id: 186248004
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.i1', '24.c1'], 'contains': ['144.bh1', '144.bz1', '144.cs1', '216.ea1', '216.eb1', '216.ec1', '216.ed1', '216.ee1', '288.cw1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [20737, 18648, 22752, 36, 15552, 20812, 16080], 'label': '31104.fx.72.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bg1', 'old_label': '72.bg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bg1', 'subgroup_fusion': None, 'weyl_group': '432.747'}
-
id: 186248005
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.j1', '24.c1'], 'contains': ['144.bi1', '144.ce1', '144.cy1', '216.ea1', '216.eg1', '216.eh1', '216.ej1', '288.cx1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [20737, 18648, 12384, 36, 15552, 76, 16080], 'label': '31104.fx.72.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bh1', 'old_label': '72.bh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bh1', 'subgroup_fusion': None, 'weyl_group': '432.747'}
-
id: 186248006
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.j1', '24.c1'], 'contains': ['144.bj1', '144.cg1', '144.cz1', '216.ea1', '216.ef1', '216.ei1', '216.ek1', '288.cx1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [20737, 18216, 12384, 36, 18144, 508, 16080], 'label': '31104.fx.72.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bi1', 'old_label': '72.bi1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bi1', 'subgroup_fusion': None, 'weyl_group': '432.747'}
-
id: 186248007
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.o1', '24.c1', '24.d1'], 'contains': ['144.f1', '144.h1', '144.l1', '144.r1', '144.bl1', '144.bs1', '144.ct1', '216.eb1', '216.ef1', '216.eg1', '216.el1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [1, 2016, 10924, 36, 10368, 3096, 15552], 'label': '31104.fx.72.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bj1', 'old_label': '72.bj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bj1', 'subgroup_fusion': None, 'weyl_group': '216.171'}
-
id: 186248008
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1', '24.e1', '36.y1'], 'contains': ['144.bm1', '144.bt1', '144.cu1', '216.ec1', '216.eh1', '216.ei1', '216.el1', '288.dc1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1, 72, 10368, 36, 18144, 10924, 2016], 'label': '31104.fx.72.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.y1', 'old_label': '72.bk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bk1', 'subgroup_fusion': None, 'weyl_group': '432.746'}
-
id: 186248009
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.p1', '24.c1', '24.f1'], 'contains': ['144.bn1', '144.bu1', '144.cv1', '216.ed1', '216.ee1', '216.ej1', '216.ek1', '216.el1', '288.dd1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [1, 18648, 10368, 36, 15552, 5712, 22752], 'label': '31104.fx.72.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bl1', 'old_label': '72.bl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bl1', 'subgroup_fusion': None, 'weyl_group': '432.746'}
-
id: 186248010
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.q1', '24.f1'], 'contains': ['144.bk1', '144.by1', '144.ck1', '216.ee1', '216.em1', '288.de1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [1, 18648, 10368, 36, 15552, 5712, 12096], 'label': '31104.fx.72.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bm1', 'old_label': '72.bm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bm1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
-
id: 186248011
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.r1', '24.d1'], 'contains': ['144.g1', '144.i1', '144.p1', '144.q1', '144.bo1', '144.cb1', '144.cn1', '216.eg1', '216.en1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [20737, 1728, 556, 36, 12384, 3096, 15552], 'label': '31104.fx.72.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bn1', 'old_label': '72.bn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bn1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
-
id: 186248012
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1', '36.z1'], 'contains': ['144.bp1', '144.cc1', '144.co1', '216.ei1', '216.eo1', '288.df1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [20737, 72, 12384, 36, 18144, 556, 1728], 'label': '31104.fx.72.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.z1', 'old_label': '72.bo1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bo1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
-
id: 186248013
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': ['2592.ff1', '2592.gc1', '2592.gb1', '2592.fb1', '2592.fl2', '2592.fl1', '2592.fv1', '2592.fh1', '2592.fj1'], 'conjugacy_class_count': 2, 'contained_in': ['4.b1', '6.b1', '6.c1', '6.j1'], 'contains': ['24.b1', '36.b1', '36.br1', '36.bt1', '36.bw1', '192.g1'], 'core': '12.c1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [12138, 15552, 10368, 15624, 76, 5712, 2592, 15984, 22752], 'label': '31104.fx.12.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': ['4.b1', '6.b1'], 'normal_contains': ['24.b1', '36.b1'], 'normalizer': '1.a1', 'old_label': '12.c1', 'projective_image': '31104.fx', 'quotient_action_image': '12.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.c1', 'subgroup_fusion': None, 'weyl_group': '10368.pi'}
-
id: 186248014
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1', '24.e1', '24.f1', '36.bc1'], 'contains': ['144.j1', '144.k1', '144.n1', '144.t1', '144.bq1', '144.br1', '144.cm1', '216.el1', '216.em1', '216.en1', '216.eo1'], 'core': '576.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1, 22752, 12096, 36, 10368, 3096, 15552], 'label': '31104.fx.72.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bc1', 'old_label': '72.bp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bp1', 'subgroup_fusion': None, 'weyl_group': '216.171'}
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id: 186248015
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1', '36.y1'], 'contains': ['144.bt1', '144.ch1', '144.cu1', '216.ep1', '216.eq1', '216.er1', '216.es1', '288.ec1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1, 72, 10368, 15588, 18144, 10924, 2016], 'label': '31104.fx.72.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.y1', 'old_label': '72.bq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bq1', 'subgroup_fusion': None, 'weyl_group': '432.746'}
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id: 186248016
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1', '36.bc1'], 'contains': ['144.m1', '144.o1', '144.s1', '144.u1', '144.br1', '144.cj1', '144.cm1', '216.ep1', '216.et1', '216.eu1', '216.ev1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1, 22752, 12096, 2628, 10368, 3096, 15552], 'label': '31104.fx.72.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bc1', 'old_label': '72.br1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.br1', 'subgroup_fusion': None, 'weyl_group': '216.171'}
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id: 186248017
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1', '36.z1'], 'contains': ['144.cc1', '144.ci1', '144.co1', '216.es1', '216.ev1', '288.ef1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [20737, 72, 12384, 15588, 18144, 556, 1728], 'label': '31104.fx.72.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.z1', 'old_label': '72.bs1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bs1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
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id: 186248018
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1', '36.y1', '36.ba1', '36.bn1'], 'contains': ['144.bm1', '144.ch1', '144.db1', '216.ew1', '216.ex1', '216.ey1', '216.fa1', '288.b1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [36, 2016, 18144, 16056, 10368, 10924, 72], 'label': '31104.fx.72.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '72.bt1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bt1', 'subgroup_fusion': None, 'weyl_group': '432.746'}
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id: 186248019
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1', '36.z1', '36.bb1', '36.bp1'], 'contains': ['144.bp1', '144.ci1', '144.dd1', '216.ey1', '216.fb1', '288.c1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [36, 12096, 18144, 504, 12384, 556, 72], 'label': '31104.fx.72.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.r1', 'old_label': '72.bu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bu1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
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id: 186248020
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1', '36.bp1'], 'contains': ['144.bp1', '144.ci2', '144.de1', '216.ey1', '216.fc1', '288.d1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [36, 12096, 18144, 3024, 12384, 556, 18216], 'label': '31104.fx.72.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bp1', 'old_label': '72.bv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bv1', 'subgroup_fusion': None, 'weyl_group': '216.99'}
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id: 186248021
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1', '36.a1', '36.bc1', '36.bd1'], 'contains': ['144.a1', '144.d1', '144.v1', '144.z1', '144.bq1', '144.cj1', '144.da1', '216.ez1', '216.fa1', '216.fb1', '216.fc1', '216.fd1'], 'core': '576.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [36, 10368, 12096, 18144, 2016, 3096, 15552], 'label': '31104.fx.72.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '72.bw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bw1', 'subgroup_fusion': None, 'weyl_group': '324.124'}
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id: 186248022
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1', '36.bc1', '36.bf1', '36.cm1'], 'contains': ['144.b1', '144.y1', '144.bd1', '144.br1', '144.da1', '216.fe1', '216.ff1', '216.fi1', '216.fj1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [10405, 15552, 10368, 16056, 1728, 2592, 22752], 'label': '31104.fx.72.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '72.bx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bx1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186248023
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1', '36.y1', '36.be1', '36.cn1'], 'contains': ['144.bt1', '144.db1', '216.fe1', '216.fg1', '216.fk1', '216.fl1', '288.g1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [10405, 72, 12940, 2664, 18144, 22752, 10368], 'label': '31104.fx.72.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '72.by1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.by1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
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id: 186248024
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': ['2592.ez1', '2592.ey1', '2592.ga1', '2592.ex1', '2592.fr1', '2592.fi1', '2592.fj1'], 'conjugacy_class_count': 2, 'contained_in': ['4.c1', '6.a1', '6.h1', '6.n1'], 'contains': ['24.a1', '36.cb1', '36.cd1', '36.cj1', '36.ck1', '36.cl1', '48.z1'], 'core': '12.d1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [6, 15552, 10368, 16056, 5712, 22752, 18144, 432, 12096], 'label': '31104.fx.12.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': ['4.c1', '6.a1'], 'normal_contains': ['24.a1'], 'normalizer': '1.a1', 'old_label': '12.d1', 'projective_image': '31104.fx', 'quotient_action_image': '12.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.d1', 'subgroup_fusion': None, 'weyl_group': '10368.pi'}
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id: 186248025
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1', '36.cp1'], 'contains': ['144.bw1', '144.dc1', '216.fe1', '216.fh1', '216.fm1', '216.fn1', '288.h1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [10405, 3096, 29404, 16056, 15552, 22752, 10368], 'label': '31104.fx.72.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cp1', 'old_label': '72.bz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bz1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186248026
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1', '36.z1', '36.bg1', '36.cu1'], 'contains': ['144.cc1', '144.dd1', '216.fi1', '216.fl1', '216.fm1', '288.i1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [10405, 72, 12384, 2664, 18144, 12940, 1728], 'label': '31104.fx.72.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '72.ca1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ca1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
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id: 186248027
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1', '36.be1', '36.bi1', '36.bn1'], 'contains': ['144.ch1', '144.db1', '216.fo1', '216.fp1', '216.fq1', '216.fs1', '288.j1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [15588, 2016, 18144, 3024, 10368, 10924, 18216], 'label': '31104.fx.72.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '72.cb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cb1', 'subgroup_fusion': None, 'weyl_group': '432.746'}
-
id: 186248028
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1', '36.bg1', '36.bh1', '36.bp1'], 'contains': ['144.ci2', '144.dd1', '216.fq1', '216.ft1', '288.k1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [15588, 12096, 18144, 504, 12384, 556, 72], 'label': '31104.fx.72.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.r1', 'old_label': '72.cc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cc1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
-
id: 186248029
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1', '36.bp1'], 'contains': ['144.ci1', '144.ci2', '144.de1', '216.fq1', '216.fu1', '288.l1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [18612, 12096, 18144, 16056, 12384, 556, 18216], 'label': '31104.fx.72.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bp1', 'old_label': '72.cd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cd1', 'subgroup_fusion': None, 'weyl_group': '216.99'}
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id: 186248030
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1', '36.a1', '36.bf1', '36.bj1'], 'contains': ['144.c1', '144.z1', '144.ba1', '144.cj1', '144.da1', '216.fr1', '216.fs1', '216.ft1', '216.fu1', '216.fv1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [18612, 10368, 12096, 18144, 2016, 3096, 15552], 'label': '31104.fx.72.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '72.ce1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ce1', 'subgroup_fusion': None, 'weyl_group': '324.124'}
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id: 186248031
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1', '36.bc1', '36.bj1', '36.cz1'], 'contains': ['144.e1', '144.bb1', '144.bf1', '144.cm1', '144.da1', '216.fw1', '216.fx1', '216.fy1', '216.ga1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1, 22752, 15552, 16056, 10368, 2592, 12096], 'label': '31104.fx.72.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '72.cf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cf1', 'subgroup_fusion': None, 'weyl_group': '144.196'}
-
id: 186248032
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1', '36.z1', '36.bh1', '36.da1'], 'contains': ['144.co1', '144.dd1', '216.fx1', '216.gc1', '288.q1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1, 72, 12384, 2664, 18144, 1728, 556], 'label': '31104.fx.72.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.r1', 'old_label': '72.cg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cg1', 'subgroup_fusion': None, 'weyl_group': '864.4000'}
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id: 186248033
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1', '36.db1'], 'contains': ['144.cq1', '144.df1', '216.fx1', '216.gd1', '288.r1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1, 72, 12384, 2664, 18144, 1728, 10924], 'label': '31104.fx.72.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.db1', 'old_label': '72.ch1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ch1', 'subgroup_fusion': None, 'weyl_group': '432.535'}
-
id: 186248034
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1', '36.y1', '36.bi1', '36.de1'], 'contains': ['144.cu1', '144.db1', '216.fz1', '216.ga1', '216.gb1', '216.gc1', '216.gd1', '288.s1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1, 72, 12384, 2664, 18144, 10924, 22752], 'label': '31104.fx.72.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '72.ci1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ci1', 'subgroup_fusion': None, 'weyl_group': None}
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id: 186248035
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': ['2592.fb1', '2592.fl2', '2592.fl1', '2592.fh1', '2592.fj1'], 'conjugacy_class_count': 1, 'contained_in': ['4.e1', '6.b1', '6.d1', '6.m1'], 'contains': ['24.b1', '36.dc1', '36.dd1', '36.de1', '36.df1', '36.dg1', '36.dh1', '48.t1'], 'core': '12.e1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 15552, 10368, 15624, 76, 22752, 18144, 15984, 5712], 'label': '31104.fx.12.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': ['4.e1', '6.b1'], 'normal_contains': ['24.b1'], 'normalizer': '1.a1', 'old_label': '12.e1', 'projective_image': '31104.fx', 'quotient_action_image': '12.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.e1', 'subgroup_fusion': None, 'weyl_group': '31104.fx'}
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id: 186248036
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1', '36.bd1', '36.bj1', '36.cm1'], 'contains': ['144.bc1', '144.bd1', '144.da1', '216.ge1', '216.gj1', '216.gl1', '216.gm1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [10837, 2592, 15552, 16056, 1728, 22752, 10368], 'label': '31104.fx.72.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '72.cj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cj1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186248037
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1', '36.bd1', '36.bf1', '36.cz1'], 'contains': ['144.be1', '144.bf1', '144.da1', '216.gf1', '216.gk1', '216.gn1', '216.go1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [433, 22752, 2592, 16056, 10368, 12096, 15552], 'label': '31104.fx.72.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '72.ck1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ck1', 'subgroup_fusion': None, 'weyl_group': '144.196'}
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id: 186248038
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1', '36.ba1', '36.bi1', '36.cn1'], 'contains': ['144.db1', '216.gg1', '216.gj1', '216.gp1', '216.gr1', '288.v1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [28981, 18216, 31084, 22752, 18144, 10368, 2592], 'label': '31104.fx.72.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '72.cl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cl1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
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id: 186248039
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1', '36.ba1', '36.be1', '36.de1'], 'contains': ['144.db1', '216.gh1', '216.gk1', '216.gq1', '216.gs1', '216.gt1', '288.w1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [18577, 18216, 12384, 2592, 18144, 29068, 22752], 'label': '31104.fx.72.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '72.cm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cm1', 'subgroup_fusion': None, 'weyl_group': None}
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id: 186248040
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1', '36.cp1'], 'contains': ['144.dc1', '216.gi1', '216.gj1', '216.gu1', '216.gv1', '288.x1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [28981, 18648, 27316, 22752, 15552, 10368, 2592], 'label': '31104.fx.72.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cp1', 'old_label': '72.cn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cn1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186248041
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1', '36.bb1', '36.bh1', '36.cu1'], 'contains': ['144.dd1', '216.gl1', '216.gr1', '216.gu1', '288.y1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [28981, 18216, 12384, 2592, 18144, 31084, 1728], 'label': '31104.fx.72.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '72.co1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.co1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
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id: 186248042
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1', '36.bb1', '36.bg1', '36.da1'], 'contains': ['144.dd1', '216.gn1', '216.gs1', '288.z1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [18577, 18216, 12384, 1728, 18144, 2592, 18700], 'label': '31104.fx.72.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.r1', 'old_label': '72.cp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cp1', 'subgroup_fusion': None, 'weyl_group': '864.4000'}
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id: 186248043
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1', '36.db1'], 'contains': ['144.df1', '216.gn1', '216.gt1', '288.ba1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [18577, 18216, 12384, 1728, 18144, 2592, 29068], 'label': '31104.fx.72.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.db1', 'old_label': '72.cq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cq1', 'subgroup_fusion': None, 'weyl_group': '432.535'}
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id: 186248044
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.a1', '36.bm1', '36.bq1', '36.bv1', '36.cb1', '36.cc1', '36.cr1', '36.cx1'], 'contains': ['216.a1', '216.gw1', '216.hb1', '288.bc1', '288.cn1', '288.co1'], 'core': '216.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [5712, 2592, 432, 12096, 15552, 10368, 15624], 'label': '31104.fx.72.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '72.cr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cr1', 'subgroup_fusion': None, 'weyl_group': '1152.155790'}
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id: 186248045
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.a1', '36.cd1', '36.ce1', '36.cy1'], 'contains': ['216.gw1', '216.gz1', '216.hb1', '288.bd1', '288.cp1', '288.cq1'], 'core': '648.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [28464, 2592, 432, 12096, 15552, 10368, 15624], 'label': '31104.fx.72.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1', 'old_label': '72.cs1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cs1', 'subgroup_fusion': None, 'weyl_group': '576.5126'}
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id: 186248046
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1'], 'contains': ['24.e1', '24.g1', '24.h1', '24.i1', '24.k1', '36.y1', '36.z1', '36.bc1', '48.a1'], 'core': '576.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1, 18144, 12096, 4032, 36, 10924, 72, 12384, 15552], 'label': '31104.fx.12.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '12.f1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1', 'subgroup_fusion': None, 'weyl_group': None}
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id: 186248047
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.b1', '36.by1', '36.cf1', '36.dc1'], 'contains': ['216.gx1', '216.gy1', '216.gz1', '216.hj1', '216.hk1', '216.hm1', '216.hn1', '216.hp1', '216.hp2', '288.be1'], 'core': '648.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [76, 18144, 18576, 28464, 15552, 10368, 16056], 'label': '31104.fx.72.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.m1', 'old_label': '72.ct1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ct1', 'subgroup_fusion': None, 'weyl_group': '576.8654'}
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id: 186248048
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.b1', '36.bk1', '36.br1', '36.bw1', '36.bz1', '36.cg1', '36.cs1', '36.dd1'], 'contains': ['216.a1', '216.gx1', '216.gy1', '216.hj1', '216.hl1', '216.hn1', '216.ho1', '288.bf1'], 'core': '216.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [76, 18144, 18576, 5712, 15552, 10368, 16056], 'label': '31104.fx.72.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '72.cu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cu1', 'subgroup_fusion': None, 'weyl_group': '1152.157852'}
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id: 186248049
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.p1', '36.bx1', '36.ch1', '36.ct1'], 'contains': ['216.a1', '216.ha1', '216.hb2', '288.bg1'], 'core': '216.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [24268, 18144, 18576, 16080, 15552, 10368, 16056], 'label': '31104.fx.72.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1', 'old_label': '72.cv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cv1', 'subgroup_fusion': None, 'weyl_group': '576.8654'}
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id: 186248050
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.p1', '36.ci1'], 'contains': ['216.gz1', '216.ha1', '216.hb2', '288.bh1'], 'core': '648.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [22828, 18144, 18576, 29904, 15552, 22752, 16056], 'label': '31104.fx.72.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.p1', 'old_label': '72.cw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cw1', 'subgroup_fusion': None, 'weyl_group': '288.1025'}
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id: 186248051
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.df1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1', '24.n1', '24.o1', '36.bn1', '36.cn1', '36.de1'], 'contains': ['144.db1', '216.b1', '216.gx1', '216.hd1', '216.he1', '216.hg1', '288.bj1'], 'core': '216.b1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [18576, 72, 10368, 15552, 18144, 10924, 22752], 'label': '31104.fx.72.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '72.cx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cx1', 'subgroup_fusion': None, 'weyl_group': '432.747'}
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id: 186248052
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.df1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1', '24.o1', '24.p1', '36.cp1'], 'contains': ['144.dc1', '216.b1', '216.ha1', '216.hh1', '216.hh2', '288.bm1'], 'core': '216.b1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [18576, 18648, 10368, 18144, 15552, 11764, 22752], 'label': '31104.fx.72.cy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1', 'old_label': '72.cy1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cy1', 'subgroup_fusion': None, 'weyl_group': '216.165'}
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id: 186248053
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.a1', '24.o1', '24.p1', '36.bu1', '36.cl1', '36.cq1'], 'contains': ['216.b1', '216.hb1', '216.hb2', '216.hi1', '288.bo1', '288.ct1'], 'core': '216.b1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [29904, 2592, 432, 22752, 15552, 10368, 15624], 'label': '31104.fx.72.cz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '72.cz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cz1', 'subgroup_fusion': None, 'weyl_group': '1728.47856'}
-
id: 186248054
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.df1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1', '36.bp1', '36.cu1', '36.da1'], 'contains': ['144.dd1', '144.de1', '216.hc1', '216.he1', '216.hh1', '288.bp1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [18576, 72, 12384, 15552, 18144, 556, 12096], 'label': '31104.fx.72.da1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '72.da1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.da1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186248055
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.df1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1', '36.db1'], 'contains': ['144.df1', '144.dg1', '216.hc1', '216.hg1', '216.hh1', '288.br1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [18576, 72, 12384, 15552, 18144, 10924, 12096], 'label': '31104.fx.72.db1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.v1', 'old_label': '72.db1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.db1', 'subgroup_fusion': None, 'weyl_group': '72.42'}
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id: 186248056
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1', '36.dg1'], 'contains': ['216.hd1', '216.hf1', '216.hg1', '216.hj1', '216.hk1', '216.hn1', '216.ho1', '216.hp1', '216.hp2', '288.bt1', '288.bv1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [76, 18144, 18576, 5712, 15552, 12384, 16056], 'label': '31104.fx.72.dc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '72.dc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dc1', 'subgroup_fusion': None, 'weyl_group': '288.1026'}
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id: 186248057
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': ['15552.c1', '15552.h1', '15552.g1', '15552.i1', '15552.e1', '15552.d1'], 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['4.b1', '4.c1', '4.d1', '6.h1', '6.i1', '6.j1', '6.k1', '32.d1'], 'core': '2.c1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [10405, 18576, 1728, 22752, 18144, 12138, 16080, 16056, 10368, 15552, 12460], 'label': '31104.fx.2.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.b1', '4.c1', '4.d1'], 'normalizer': '1.a1', 'old_label': '2.c1', 'projective_image': '31104.fx', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1', 'subgroup_fusion': None, 'weyl_group': '10368.pi'}
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id: 186248058
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1'], 'contains': ['24.h1', '24.l1', '24.m1', '36.ba1', '36.bb1', '36.bd1', '48.b1'], 'core': '576.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [18577, 18144, 12096, 4032, 36, 29068, 18216, 12384, 2592], 'label': '31104.fx.12.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '12.g1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1', 'subgroup_fusion': None, 'weyl_group': None}
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id: 186248059
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1', '36.cv1'], 'contains': ['216.he1', '216.hh2', '216.hi1', '288.bu1', '288.bx1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [21100, 18144, 18576, 29904, 15552, 12384, 16056], 'label': '31104.fx.72.dd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1', 'old_label': '72.dd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dd1', 'subgroup_fusion': None, 'weyl_group': '288.1026'}
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id: 186248060
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1', '36.bl1', '36.cw1', '36.dh1'], 'contains': ['216.hd1', '216.he1', '216.hf1', '216.hj1', '216.hk1', '216.hl1', '216.hm1', '288.bw1', '288.by1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [20812, 18144, 18576, 5712, 15552, 12384, 16056], 'label': '31104.fx.72.de1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '72.de1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.de1', 'subgroup_fusion': None, 'weyl_group': '576.8657'}
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id: 186248061
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1'], 'contains': ['216.hg1', '216.hh2', '216.hi1', '288.bz1', '288.ca1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [364, 18144, 18576, 29904, 15552, 12384, 16056], 'label': '31104.fx.72.df1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.o1', 'old_label': '72.df1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.df1', 'subgroup_fusion': None, 'weyl_group': '144.184'}
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id: 186248062
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.c1', '36.dk1', '36.dl1'], 'contains': ['144.dh1', '144.di1', '144.dj1', '144.do1', '144.dr1', '144.dw1', '144.dz1', '216.hq1', '216.hs1', '216.ht1'], 'core': '576.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [5713, 22752, 12096, 2598, 10368, 36, 18576], 'label': '31104.fx.72.dg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '72.dg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dg1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
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id: 186248063
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.d1', '36.dk1', '36.dl1'], 'contains': ['144.dh1', '144.dj1', '144.dk1', '144.ds1', '144.dt1', '144.ea1', '144.eb1', '216.hr1', '216.hu1', '216.hv1'], 'core': '576.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [8305, 22752, 12096, 2598, 10368, 36, 18576], 'label': '31104.fx.72.dh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '72.dh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dh1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
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id: 186248064
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1', '36.dl1'], 'contains': ['144.dh1', '144.di1', '144.dl1', '144.du1', '144.ec1', '144.ga1', '144.gb1', '216.hw1', '216.hy1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [5713, 22752, 12096, 6, 10368, 36, 18576], 'label': '31104.fx.72.di1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '72.di1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.di1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
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id: 186248065
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.d1', '36.dl1'], 'contains': ['144.dh1', '144.dk1', '144.dn1', '144.dv1', '144.ed1', '216.hx1', '216.hz1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [8305, 22752, 12096, 6, 10368, 36, 18576], 'label': '31104.fx.72.dj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '72.dj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dj1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
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id: 186248066
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1', '36.dk1'], 'contains': ['144.di1', '144.dj1', '144.eg1', '144.ek1', '144.el1', '216.ia1', '216.ib1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [5713, 22752, 12096, 78, 10368, 36, 18576], 'label': '31104.fx.72.dk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '72.dk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dk1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
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id: 186248067
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.d1', '36.dk1'], 'contains': ['144.dj1', '144.dk1', '144.em1', '144.en1', '144.eo1', '216.ic1', '216.id1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [8305, 22752, 12096, 78, 10368, 36, 18576], 'label': '31104.fx.72.dl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '72.dl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dl1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
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id: 186248068
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.c1', '36.dm1', '36.dn1'], 'contains': ['144.dl1', '144.dp1', '144.dr1', '144.dx1', '144.dz1', '144.ee1', '144.eg1', '216.ie1', '216.ik1', '216.io1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [5713, 22752, 12096, 2598, 10368, 108, 18576], 'label': '31104.fx.72.dm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '72.dm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dm1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
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id: 186248069
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1'], 'contains': ['24.i1', '24.j1', '24.m1', '36.be1', '36.bf1', '36.bg1', '48.c1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [18577, 18144, 12096, 4032, 18612, 29068, 18216, 12384, 2592], 'label': '31104.fx.12.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '12.h1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1', 'subgroup_fusion': None, 'weyl_group': None}
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id: 186248070
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.d1', '36.dm1', '36.dn1'], 'contains': ['144.dn1', '144.dp1', '144.ds1', '144.dx1', '144.eb1', '144.eh1', '144.em1', '216.if1', '216.il1', '216.ip1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [8305, 22752, 12096, 2598, 10368, 108, 18576], 'label': '31104.fx.72.dn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '72.dn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dn1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
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id: 186248071
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.e1', '36.dl1', '36.dm1'], 'contains': ['144.dl1', '144.dm1', '144.ds1', '144.dw1', '144.dy1', '144.ed1', '144.ef1', '216.ig1', '216.im1', '216.iq1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [8305, 22752, 12096, 6, 10368, 2700, 18576], 'label': '31104.fx.72.do1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '72.do1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.do1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
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id: 186248072
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.f1', '36.dl1', '36.dm1'], 'contains': ['144.dm1', '144.dn1', '144.dr1', '144.dy1', '144.ea1', '144.ec1', '144.ei1', '216.ih1', '216.in1', '216.ir1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [5713, 22752, 12096, 6, 10368, 2700, 18576], 'label': '31104.fx.72.dp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '72.dp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dp1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
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id: 186248073
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.e1', '36.dk1', '36.dn1'], 'contains': ['144.do1', '144.dq1', '144.ds1', '144.ef1', '144.eg1', '144.ej1', '144.eo1', '216.ii1', '216.is1', '216.it1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [8305, 22752, 12096, 78, 10368, 2628, 18576], 'label': '31104.fx.72.dq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '72.dq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dq1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
-
id: 186248074
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.f1', '36.dk1', '36.dn1'], 'contains': ['144.dq1', '144.dr1', '144.dt1', '144.ei1', '144.ej1', '144.el1', '144.em1', '216.ij1', '216.iu1', '216.iv1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [5713, 22752, 12096, 78, 10368, 2628, 18576], 'label': '31104.fx.72.dr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '72.dr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dr1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
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id: 186248075
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.e1', '36.dl1', '36.dn1'], 'contains': ['144.dl1', '144.dm1', '144.do1', '144.dq1', '144.dv1', '144.eb1', '144.ef1', '216.iw1', '216.iy1', '216.jc1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [8305, 22752, 12096, 2670, 10368, 2700, 18576], 'label': '31104.fx.72.ds1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '72.ds1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ds1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
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id: 186248076
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.f1', '36.dl1', '36.dn1'], 'contains': ['144.dm1', '144.dn1', '144.dq1', '144.dt1', '144.du1', '144.dz1', '144.ei1', '216.ix1', '216.iz1', '216.jd1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [5713, 22752, 12096, 2670, 10368, 2700, 18576], 'label': '31104.fx.72.dt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '72.dt1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dt1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
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id: 186248077
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1', '36.dn1'], 'contains': ['144.do1', '144.dp1', '144.du1', '144.ee1', '144.el1', '216.ja1', '216.je1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [5713, 22752, 12096, 78, 10368, 108, 18576], 'label': '31104.fx.72.du1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '72.du1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.du1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
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id: 186248078
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.dv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.d1', '36.dn1'], 'contains': ['144.dp1', '144.dt1', '144.dv1', '144.eh1', '144.eo1', '216.jb1', '216.jf1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [8305, 22752, 12096, 78, 10368, 108, 18576], 'label': '31104.fx.72.dv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '72.dv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dv1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
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id: 186248079
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.e1', '36.dk1', '36.dm1'], 'contains': ['144.dw1', '144.dy1', '144.eb1', '144.ef1', '144.eg1', '144.ej1', '144.en1', '216.jg1', '216.jh1', '216.jm1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [8305, 22752, 12096, 2598, 10368, 2700, 18576], 'label': '31104.fx.72.dw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '72.dw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dw1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
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id: 186248080
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1'], 'contains': ['24.j1', '24.k1', '24.l1', '36.bh1', '36.bi1', '36.bj1', '48.d1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1, 18144, 12096, 4032, 18612, 10924, 18216, 12384, 2592], 'label': '31104.fx.12.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '12.i1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.i1', 'subgroup_fusion': None, 'weyl_group': None}
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id: 186248081
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.dx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.f1', '36.dk1', '36.dm1'], 'contains': ['144.dy1', '144.dz1', '144.ea1', '144.ei1', '144.ej1', '144.ek1', '144.em1', '216.ji1', '216.jj1', '216.jn1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [5713, 22752, 12096, 2670, 10368, 2628, 18576], 'label': '31104.fx.72.dx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '72.dx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dx1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
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id: 186248082
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1', '36.dm1'], 'contains': ['144.dw1', '144.dx1', '144.ec1', '144.ee1', '144.ek1', '216.jk1', '216.jo1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [5713, 22752, 12096, 6, 10368, 108, 18576], 'label': '31104.fx.72.dy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '72.dy1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dy1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
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id: 186248083
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.d1', '36.dm1'], 'contains': ['144.dx1', '144.ea1', '144.ed1', '144.eh1', '144.en1', '216.jl1', '216.jp1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [8305, 22752, 12096, 6, 10368, 108, 18576], 'label': '31104.fx.72.dz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '72.dz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dz1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
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id: 186248084
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.k1', '24.q1', '36.di1'], 'contains': ['144.ep1', '144.et1', '144.fj1', '216.jq1', '216.jy1', '288.cy1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [6, 12096, 18576, 36, 22752, 20812, 2664], 'label': '31104.fx.72.ea1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.di1', 'old_label': '72.ea1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ea1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
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id: 186248085
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.eb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.l1', '24.q1', '36.dj1'], 'contains': ['144.er1', '144.ew1', '144.fb1', '216.jq1', '216.js1', '216.kd1', '288.cz1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [19135, 22752, 2592, 36, 10368, 5712, 15984], 'label': '31104.fx.72.eb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.dj1', 'old_label': '72.eb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.eb1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
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id: 186248086
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.ec1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.m1', '24.r1', '36.di1'], 'contains': ['144.ep1', '144.ey1', '144.fc1', '216.jt1', '216.jz1', '288.da1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [6, 18576, 10368, 36, 2592, 5712, 12096], 'label': '31104.fx.72.ec1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.di1', 'old_label': '72.ec1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ec1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
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id: 186248087
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.ed1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.m1', '24.r1'], 'contains': ['144.eq1', '144.ez1', '144.fd1', '216.jt1', '216.ka1', '288.da1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [26047, 15624, 22752, 36, 15984, 23836, 12096], 'label': '31104.fx.72.ed1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.ed1', 'old_label': '72.ed1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ed1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
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id: 186248088
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.ee1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.n1', '24.r1', '36.dj1'], 'contains': ['144.er1', '144.fa1', '144.fh1', '216.jr1', '216.jt1', '216.kb1', '288.db1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [24198, 16056, 10368, 36, 432, 456, 22752], 'label': '31104.fx.72.ee1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.dj1', 'old_label': '72.ee1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ee1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
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id: 186248089
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.ef1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.p1', '24.s1', '36.dj1'], 'contains': ['144.er1', '144.fn1', '144.fu1', '216.ju1', '216.jv1', '216.jw1', '216.ke1', '288.dd1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [1, 432, 10368, 36, 2592, 76, 12384], 'label': '31104.fx.72.ef1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.dj1', 'old_label': '72.ef1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ef1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
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id: 186248090
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.eg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.q1', '24.s1', '36.di1'], 'contains': ['144.ep1', '144.fp1', '144.fr1', '216.jv1', '216.kg1', '288.de1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [1, 18576, 10368, 36, 2592, 5712, 12096], 'label': '31104.fx.72.eg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.di1', 'old_label': '72.eg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.eg1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
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id: 186248091
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '6.c1', '6.d1'], 'contains': ['24.b1', '36.bk1', '36.bl1', '36.bn1', '36.bo1', '48.e1'], 'core': '24.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [36, 10368, 18576, 18144, 76, 16056, 12384, 15552, 5712], 'label': '31104.fx.12.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.j1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.j1', 'subgroup_fusion': None, 'weyl_group': '10368.fj'}
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id: 186248092
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.eh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.r1', '36.g1', '36.dk1', '36.dl1'], 'contains': ['144.dh1', '144.dj1', '144.dq1', '144.dy1', '144.es1', '144.eu1', '144.fg1', '216.jx1', '216.jz1', '216.ka1', '216.kb1'], 'core': '576.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [26047, 22752, 12096, 36, 10368, 16056, 18576], 'label': '31104.fx.72.eh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '72.eh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.eh1', 'subgroup_fusion': None, 'weyl_group': '432.759'}
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id: 186248093
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.ei1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.q1', '36.g1', '36.dl1'], 'contains': ['144.dh1', '144.dm1', '144.es1', '144.ev1', '144.fl1', '216.jy1', '216.kc1', '216.kd1'], 'core': '576.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [6, 10368, 12096, 36, 22752, 16056, 18576], 'label': '31104.fx.72.ei1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '72.ei1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ei1', 'subgroup_fusion': None, 'weyl_group': '2592.jb'}
-
id: 186248094
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.s1', '36.h1', '36.dk1', '36.dl1'], 'contains': ['144.di1', '144.dk1', '144.ef1', '144.ei1', '144.es1', '144.fm1', '144.ft1', '216.ke1', '216.kf1', '216.kg1', '216.kh1'], 'core': '576.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1, 22752, 12096, 36, 10368, 3024, 2592], 'label': '31104.fx.72.ej1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '72.ej1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ej1', 'subgroup_fusion': None, 'weyl_group': '432.759'}
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id: 186248095
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.g1', '36.i1', '36.dk1'], 'contains': ['144.dj1', '144.ej1', '144.es1', '144.fv1', '144.fw1', '216.ki1', '216.kj1', '216.kk1', '216.kl1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [18150, 10368, 12096, 36, 22752, 18576, 16056], 'label': '31104.fx.72.ek1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '72.ek1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ek1', 'subgroup_fusion': None, 'weyl_group': '864.4406'}
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id: 186248096
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.el1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.u1', '24.t1', '36.di1'], 'contains': ['144.et1', '144.fc1', '144.fp1', '216.kq1', '216.kr1', '216.ks1', '288.di1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [26485, 2664, 22752, 12138, 18576, 28012, 12096], 'label': '31104.fx.72.el1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.di1', 'old_label': '72.el1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.el1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186248097
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.em1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.g1', '36.dm1', '36.dn1'], 'contains': ['144.dm1', '144.dp1', '144.dx1', '144.ej1', '144.eu1', '144.fg1', '144.fq1', '216.kn1', '216.kv1', '216.kw1', '216.kx1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [26047, 22752, 12096, 2628, 10368, 16056, 18576], 'label': '31104.fx.72.em1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '72.em1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.em1', 'subgroup_fusion': None, 'weyl_group': '432.759'}
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id: 186248098
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.en1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.u1', '36.k1', '36.dl1', '36.dm1'], 'contains': ['144.dl1', '144.dn1', '144.dw1', '144.ea1', '144.eu1', '144.fl1', '144.fm1', '216.km1', '216.ky1', '216.kz1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [26485, 12096, 18576, 6, 22752, 16056, 10368], 'label': '31104.fx.72.en1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '72.en1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.en1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186248099
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.eo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.k1', '36.dk1', '36.dn1'], 'contains': ['144.do1', '144.dt1', '144.eg1', '144.em1', '144.eu1', '144.fm1', '144.fw1', '216.ko1', '216.la1', '216.lb1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [26485, 12096, 18576, 2598, 22752, 16056, 10368], 'label': '31104.fx.72.eo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '72.eo1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.eo1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186248100
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.ep1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.o1', '36.dk1', '36.dm1'], 'contains': ['144.dr1', '144.ds1', '144.ek1', '144.en1', '144.eu1', '144.ft1', '144.fv1', '216.kp1', '216.lc1', '216.ld1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [5713, 22752, 18576, 12210, 10368, 2592, 12096], 'label': '31104.fx.72.ep1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '72.ep1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ep1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186248101
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.eq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.t1', '36.k1', '36.dl1', '36.dn1'], 'contains': ['144.dl1', '144.dn1', '144.do1', '144.dt1', '144.ev1', '144.fg1', '144.fm1', '216.kq1', '216.lf1', '216.lg1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [26485, 12096, 18576, 6, 22752, 2592, 10368], 'label': '31104.fx.72.eq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '72.eq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.eq1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186248102
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '6.f1'], 'contains': ['24.h1', '24.j1', '24.n1', '36.a1', '36.bn1', '36.bp1', '48.f1'], 'core': '36.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [36, 10368, 72, 18144, 18576, 10924, 2016, 12096, 15552], 'label': '31104.fx.12.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '12.k1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.k1', 'subgroup_fusion': None, 'weyl_group': None}
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id: 186248103
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.er1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.x1', '24.t1', '36.dj1'], 'contains': ['144.ew1', '144.fh1', '144.fn1', '216.kr1', '216.lf1', '216.lh1', '288.dl1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [26485, 2664, 10368, 12138, 18576, 22752, 28012], 'label': '31104.fx.72.er1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.dj1', 'old_label': '72.er1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.er1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
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id: 186248104
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.es1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.y1', '24.t1'], 'contains': ['144.ex1', '144.fi1', '144.fo1', '216.ks1', '216.lf1', '216.li1', '288.dm1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [13861, 18576, 22752, 6, 2592, 10368, 19536], 'label': '31104.fx.72.es1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.es1', 'old_label': '72.es1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.es1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186248105
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.et1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.g1', '36.l1', '36.dn1'], 'contains': ['144.dp1', '144.dq1', '144.ev1', '144.fq1', '144.fw1', '216.kt1', '216.lj1', '216.lj2', '216.lk1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [10855, 22752, 12096, 16092, 10368, 2592, 18576], 'label': '31104.fx.72.et1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '72.et1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.et1', 'subgroup_fusion': None, 'weyl_group': '864.4406'}
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id: 186248106
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.eu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.ba1', '24.u1', '36.dj1'], 'contains': ['144.fa1', '144.fb1', '144.fn1', '216.ku1', '216.ky1', '216.lm1', '288.dp1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [10405, 18576, 10368, 12138, 2592, 22752, 16080], 'label': '31104.fx.72.eu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.dj1', 'old_label': '72.eu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.eu1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
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id: 186248107
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.ev1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.bb1', '24.u1', '36.di1'], 'contains': ['144.ey1', '144.fj1', '144.fp1', '216.kz1', '216.lm1', '288.dq1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [10405, 18576, 10368, 12138, 2592, 16080, 1728], 'label': '31104.fx.72.ev1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.x1', 'old_label': '72.ev1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ev1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
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id: 186248108
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.ew1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.v1', '36.o1', '36.dl1', '36.dn1'], 'contains': ['144.dr1', '144.ds1', '144.du1', '144.dv1', '144.eu1', '144.ev1', '144.ft1', '216.le1', '216.ll1', '216.lo1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [5713, 22752, 18576, 12138, 10368, 2592, 12096], 'label': '31104.fx.72.ew1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '72.ew1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ew1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186248148
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '96.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.u1', '32.d1', '48.bd1'], 'contains': ['192.f1', '192.i1', '192.n1', '288.dk1', '288.dp1', '288.dq1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [10405, 10368, 1728, 12138, 22752, 16080], 'label': '31104.fx.96.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bd1', 'old_label': '96.v1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.v1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
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id: 186248109
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.ex1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.be1', '24.v1', '36.di1'], 'contains': ['144.et1', '144.ey1', '144.fr1', '216.le1', '216.lp1', '288.dt1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [5713, 2664, 22752, 12138, 18576, 12096, 5260], 'label': '31104.fx.72.ex1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.di1', 'old_label': '72.ex1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ex1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
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id: 186248110
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.ey1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.bg1', '24.v1', '36.dj1'], 'contains': ['144.ew1', '144.fa1', '144.fu1', '216.ln1', '216.lo1', '216.lp1', '288.dv1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [1, 18576, 10368, 12138, 2592, 5712, 22752], 'label': '31104.fx.72.ey1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.x1', 'old_label': '72.ey1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ey1', 'subgroup_fusion': None, 'weyl_group': '2592.jb'}
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id: 186248111
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.ez1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.k1', '36.dk1', '36.dm1'], 'contains': ['144.dw1', '144.ea1', '144.eg1', '144.em1', '144.fg1', '144.fm1', '144.fv1', '216.lq1', '216.lr1', '216.lx1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [26485, 12096, 18576, 78, 22752, 2592, 10368], 'label': '31104.fx.72.ez1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '72.ez1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ez1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186248112
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.fa1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.s1', '36.dk1', '36.dn1'], 'contains': ['144.dz1', '144.eb1', '144.el1', '144.eo1', '144.fg1', '144.ft1', '144.fw1', '216.ls1', '216.lt1', '216.ly1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [5713, 22752, 12096, 78, 10368, 2592, 18576], 'label': '31104.fx.72.fa1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '72.fa1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fa1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
-
id: 186248113
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '12.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.b1', '6.e1', '6.h1', '6.l1'], 'contains': ['24.a1', '36.bq1', '36.bs1', '36.bt1', '36.bu1', '48.w1'], 'core': '24.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [12138, 10368, 2664, 18576, 76, 22752, 15552, 2592, 12096], 'label': '31104.fx.12.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.l1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.l1', 'subgroup_fusion': None, 'weyl_group': '3456.de'}
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id: 186248114
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.fb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.bj1', '24.w1', '36.dj1'], 'contains': ['144.fb1', '144.fh1', '144.fu1', '216.lz1', '216.ma1', '216.mb1', '216.mc1', '288.dy1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [1, 18576, 10368, 6, 2592, 5712, 22752], 'label': '31104.fx.72.fb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.dj1', 'old_label': '72.fb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fb1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
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id: 186248115
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.fc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.g1', '36.p1', '36.dm1'], 'contains': ['144.dx1', '144.dy1', '144.fl1', '144.fq1', '144.fv1', '216.lu1', '216.lv1', '216.lw1', '216.me1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [26047, 22752, 12096, 16092, 10368, 2592, 18576], 'label': '31104.fx.72.fc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '72.fc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fc1', 'subgroup_fusion': None, 'weyl_group': '864.4406'}
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id: 186248116
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.fd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.bk1', '24.w1', '36.di1'], 'contains': ['144.fc1', '144.fj1', '144.fr1', '216.lz1', '216.mf1', '288.dz1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [1, 18576, 10368, 6, 2592, 5712, 12096], 'label': '31104.fx.72.fd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.di1', 'old_label': '72.fd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fd1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
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id: 186248117
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.fe1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.bl1', '24.w1'], 'contains': ['144.fe1', '144.fk1', '144.fs1', '216.ma1', '216.mf1', '288.ea1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [5713, 2664, 22752, 6, 18576, 15628, 12096], 'label': '31104.fx.72.fe1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.fe1', 'old_label': '72.fe1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fe1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
-
id: 186248118
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.ff1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.w1', '36.s1', '36.dl1', '36.dm1'], 'contains': ['144.dz1', '144.eb1', '144.ec1', '144.ed1', '144.fg1', '144.fl1', '144.ft1', '216.mb1', '216.md1', '216.mf1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [5713, 22752, 12096, 6, 10368, 2592, 18576], 'label': '31104.fx.72.ff1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '72.ff1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ff1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
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id: 186248119
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.fg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.h1', '36.dm1', '36.dn1'], 'contains': ['144.ee1', '144.ef1', '144.eh1', '144.ei1', '144.fm1', '144.fq1', '144.ft1', '216.mg1', '216.mh1', '216.mi1', '216.mj1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1, 22752, 12096, 15588, 10368, 3024, 2592], 'label': '31104.fx.72.fg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '72.fg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fg1', 'subgroup_fusion': None, 'weyl_group': '432.759'}
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id: 186248120
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '72.fh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.i1', '36.l1', '36.p1'], 'contains': ['144.fq1', '144.fv1', '144.fw1', '216.mk1', '216.ml1', '216.mm1', '216.mm2', '216.mn1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [15558, 10368, 12096, 18180, 22752, 2664, 18576], 'label': '31104.fx.72.fh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.s1', 'old_label': '72.fh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fh1', 'subgroup_fusion': None, 'weyl_group': '432.768'}
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id: 186248121
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '81.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['27.a1', '27.b1', '27.c1'], 'contains': ['162.o1', '162.p1', '162.r1', '162.ba1', '162.bd1', '162.bg1', '162.bi1', '243.a1', '324.el1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [20737, 16056, 432, 24198, 16080, 15552, 2592, 36], 'label': '31104.fx.81.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '81.a1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.a1', 'subgroup_fusion': None, 'weyl_group': '192.955'}
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id: 186248122
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '81.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.d1'], 'contains': ['162.b1', '162.c1', '162.g1', '162.i1', '162.j1', '162.n1', '162.t1', '162.x1', '162.z1', '162.bc1', '162.bk1', '243.a1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [5713, 72, 2592, 6, 15552, 12096, 18576, 36], 'label': '31104.fx.81.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '81.b1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.b1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
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id: 186248123
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '81.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['27.b1', '27.c1', '27.d1', '27.e1'], 'contains': ['162.a1', '162.d1', '162.e1', '162.f1', '162.h1', '162.k1', '162.l1', '162.m1', '162.s1', '162.u1', '162.v1', '162.y1', '162.be1', '162.bf1', '162.bh1', '243.a1'], 'core': '648.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [5713, 72, 2592, 24198, 15552, 22752, 18576, 36], 'label': '31104.fx.81.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '81.c1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.c1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
-
id: 186248124
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '12.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.b1', '6.k1'], 'contains': ['24.p1', '36.b1', '36.bu1', '36.bx1', '192.h1'], 'core': '36.b1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [17371, 15552, 22752, 16056, 29904, 23836, 18144, 18576, 10368], 'label': '31104.fx.12.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '12.m1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.m1', 'subgroup_fusion': None, 'weyl_group': '5184.ov'}
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id: 186248125
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '96.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1', '48.a1', '48.b1', '48.f1'], 'contains': ['192.a1', '192.c1', '192.r1', '288.b1', '288.c1', '288.d1', '288.e1'], 'core': '576.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [36, 12384, 4032, 3096, 10924, 12096], 'label': '31104.fx.96.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.d1', 'old_label': '96.a1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.a1', 'subgroup_fusion': None, 'weyl_group': '324.124'}
-
id: 186248126
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '96.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1', '48.a1', '48.c1', '48.i1'], 'contains': ['192.a1', '192.m1', '288.f1', '288.g1', '288.h1', '288.i1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [10405, 12384, 1728, 15552, 10368, 12940], 'label': '31104.fx.96.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.d1', 'old_label': '96.b1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.b1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186248127
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '96.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1', '48.c1', '48.d1', '48.f1'], 'contains': ['192.a1', '192.r1', '288.j1', '288.k1', '288.l1', '288.n1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [15588, 12384, 4032, 3096, 10924, 12096], 'label': '31104.fx.96.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.d1', 'old_label': '96.c1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.c1', 'subgroup_fusion': None, 'weyl_group': '324.124'}
-
id: 186248128
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '96.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1', '48.a1', '48.d1', '48.q1'], 'contains': ['192.a1', '192.s1', '288.p1', '288.q1', '288.r1', '288.s1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [1, 12384, 10368, 15552, 12096, 10924], 'label': '31104.fx.96.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.d1', 'old_label': '96.d1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.d1', 'subgroup_fusion': None, 'weyl_group': '648.610'}
-
id: 186248129
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '96.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1', '48.b1', '48.d1', '48.i1'], 'contains': ['192.a1', '288.t1', '288.v1', '288.x1', '288.y1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [10909, 12384, 1728, 10368, 15552, 31084], 'label': '31104.fx.96.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.d1', 'old_label': '96.e1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.e1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 186248130
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '96.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1', '48.b1', '48.c1', '48.q1'], 'contains': ['192.a1', '288.u1', '288.w1', '288.z1', '288.ba1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [505, 12384, 10368, 12096, 15552, 29068], 'label': '31104.fx.96.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.d1', 'old_label': '96.f1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.f1', 'subgroup_fusion': None, 'weyl_group': '648.610'}
-
id: 186248131
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '96.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.df1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1', '32.a1', '48.f1', '48.i1', '48.q1'], 'contains': ['192.a1', '288.bi1', '288.bj1', '288.bm1', '288.bp1', '288.br1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [3096, 12384, 10368, 15552, 10924, 12096], 'label': '31104.fx.96.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1', 'old_label': '96.g1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.g1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
-
id: 186248132
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '96.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.df1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1', '48.g1', '48.j1', '48.p1', '48.r1', '48.u1'], 'contains': ['288.bi1', '288.bk1', '288.bn1', '288.bq1', '288.bs1', '384.a1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [28996, 18144, 72, 12096, 10368, 12384], 'label': '31104.fx.96.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '96.h1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.h1', 'subgroup_fusion': None, 'weyl_group': '432.747'}
-
id: 186248133
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '96.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.a1', '32.a1', '48.h1', '48.k1', '48.s1'], 'contains': ['288.bc1', '288.bd1', '288.bi1', '288.bl1', '288.bo1', '384.b1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [76, 15552, 18648, 12096, 10368, 22752], 'label': '31104.fx.96.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1', 'old_label': '96.i1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.i1', 'subgroup_fusion': None, 'weyl_group': '432.747'}
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id: 186248134
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '96.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1', '32.a1', '48.l1'], 'contains': ['288.bj1', '288.bn1', '288.bo1', '288.bu1', '288.bz1', '384.c1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [24268, 15552, 18648, 29904, 10368, 12384], 'label': '31104.fx.96.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1', 'old_label': '96.j1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.j1', 'subgroup_fusion': None, 'weyl_group': '216.165'}
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id: 186248135
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '12.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.c1', '6.e1', '6.i1', '6.n1'], 'contains': ['24.a1', '36.ca1', '36.cc1', '36.ce1', '36.cj1', '48.y1'], 'core': '24.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [6, 22752, 18576, 2592, 76, 2664, 12096, 15552, 10368], 'label': '31104.fx.12.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.n1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.n1', 'subgroup_fusion': None, 'weyl_group': '3456.gu'}
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id: 186248136
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '96.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1', '32.a1', '48.m1'], 'contains': ['288.bk1', '288.bm1', '288.bo1', '288.bx1', '288.ca1', '384.c1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [24700, 18144, 72, 29904, 10368, 12384], 'label': '31104.fx.96.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1', 'old_label': '96.k1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.k1', 'subgroup_fusion': None, 'weyl_group': '216.165'}
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id: 186248137
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '96.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1', '32.a1', '48.e1', '48.n1', '48.t1'], 'contains': ['288.be1', '288.bf1', '288.bj1', '288.bk1', '288.bl1', '288.bt1', '288.bv1', '288.bw1', '288.by1', '384.d1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [76, 15552, 18648, 5712, 22752, 10368], 'label': '31104.fx.96.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1', 'old_label': '96.l1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.l1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
-
id: 186248138
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '96.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.p1', '32.a1', '48.o1'], 'contains': ['288.bg1', '288.bh1', '288.bl1', '288.bm1', '288.bn1', '288.bo1', '384.e1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [76, 15552, 18648, 29904, 10368, 22752], 'label': '31104.fx.96.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1', 'old_label': '96.m1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.m1', 'subgroup_fusion': None, 'weyl_group': '216.165'}
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id: 186248139
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '96.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.a1', '48.v1', '48.w1', '48.x1', '48.y1', '48.z1', '48.ba1', '48.bb1'], 'contains': ['288.cn1', '288.co1', '288.cp1', '288.cq1', '288.cr1', '288.cs1', '288.ct1', '384.b1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [76, 18576, 2664, 12096, 10368, 22752], 'label': '31104.fx.96.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.x1', 'old_label': '96.n1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.n1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
-
id: 186248140
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '96.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.c1', '32.b1', '48.bc1'], 'contains': ['192.b1', '192.g1', '192.j1', '288.cu1', '288.cv1', '288.cz1', '288.db1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [19135, 10368, 22752, 36, 8304, 25852], 'label': '31104.fx.96.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bc1', 'old_label': '96.o1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.o1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
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id: 186248141
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '96.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1', '32.c1', '48.bc1'], 'contains': ['192.b1', '192.p1', '192.u1', '288.cw1', '288.cx1', '288.dc1', '288.dd1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [1, 10368, 12384, 36, 18580, 5712], 'label': '31104.fx.96.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bc1', 'old_label': '96.p1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.p1', 'subgroup_fusion': None, 'weyl_group': '648.734'}
-
id: 186248142
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '96.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.q1', '32.b1', '48.bd1'], 'contains': ['192.d1', '192.e1', '192.i1', '288.cy1', '288.cz1', '288.dg1'], 'core': '576.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [2670, 22752, 24768, 36, 76, 12096], 'label': '31104.fx.96.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bd1', 'old_label': '96.q1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.q1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
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id: 186248143
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '96.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.r1', '32.b1', '48.bd1'], 'contains': ['192.d1', '192.f1', '192.l1', '288.da1', '288.db1', '288.dg1'], 'core': '576.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [6, 10368, 22752, 36, 5712, 12096], 'label': '31104.fx.96.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.d1', 'old_label': '96.r1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.r1', 'subgroup_fusion': None, 'weyl_group': '1944.2342'}
-
id: 186248144
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '96.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1', '32.c1', '48.a1'], 'contains': ['192.c1', '192.m1', '192.s1', '288.dc1', '288.df1', '288.dh1'], 'core': '576.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [1, 12384, 4032, 36, 10924, 12096], 'label': '31104.fx.96.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.a1', 'old_label': '96.s1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.s1', 'subgroup_fusion': None, 'weyl_group': '324.124'}
-
id: 186248145
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '96.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.f1', '24.s1', '32.c1', '48.bd1'], 'contains': ['192.d1', '192.n1', '192.t1', '288.dd1', '288.de1', '288.dh1'], 'core': '576.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [1, 10368, 22752, 36, 5712, 12096], 'label': '31104.fx.96.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bd1', 'old_label': '96.t1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.t1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
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id: 186248146
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '12.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.c1', '6.c1', '6.j1', '6.m1'], 'contains': ['24.b1', '36.by1', '36.bz1', '36.ca1', '36.cf1', '36.cg1', '36.ck1', '192.j1'], 'core': '24.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [6, 15552, 22752, 15624, 76, 5712, 2592, 15984, 10368], 'label': '31104.fx.12.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.o1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.o1', 'subgroup_fusion': None, 'weyl_group': '3456.di'}
-
id: 186248147
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '96.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.t1', '32.d1', '48.bd1'], 'contains': ['192.e1', '192.l1', '192.n1', '288.di1', '288.dk1', '288.dl1', '288.dm1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [26485, 22752, 10368, 30714, 28012, 12096], 'label': '31104.fx.96.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bd1', 'old_label': '96.u1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.u1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
-
id: 186248149
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '96.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.j1', '32.d1', '48.bc1'], 'contains': ['192.g1', '192.j1', '192.p1', '288.dj1', '288.dl1', '288.dp1', '288.dr1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [10405, 10368, 16080, 12138, 22752, 30964], 'label': '31104.fx.96.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bc1', 'old_label': '96.w1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.w1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
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id: 186248150
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '96.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.k1', '32.d1'], 'contains': ['192.h1', '192.k1', '192.q1', '288.dm1', '288.dp1', '288.ds1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [13861, 22752, 19536, 6, 10368, 16564], 'label': '31104.fx.96.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.x1', 'old_label': '96.x1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.x1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
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id: 186248151
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '96.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.v1', '32.e1', '48.bd1'], 'contains': ['192.e1', '192.f1', '192.t1', '288.do1', '288.dt1', '288.dv1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [1, 10368, 22752, 12138, 12096, 5712], 'label': '31104.fx.96.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bd1', 'old_label': '96.y1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.y1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
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id: 186248152
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '96.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1', '32.e1', '48.bc1'], 'contains': ['192.g1', '192.u1', '288.du1', '288.dv1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [1, 10368, 22752, 12138, 18580, 5712], 'label': '31104.fx.96.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.d1', 'old_label': '96.z1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.z1', 'subgroup_fusion': None, 'weyl_group': '1944.2342'}
-
id: 186248153
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '96.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.m1', '32.f1', '48.bc1'], 'contains': ['192.j1', '192.u1', '288.dw1', '288.dx1', '288.dy1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [1, 10368, 22752, 6, 18580, 5712], 'label': '31104.fx.96.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bc1', 'old_label': '96.ba1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ba1', 'subgroup_fusion': None, 'weyl_group': '648.734'}
-
id: 186248154
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '96.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.w1', '32.f1', '48.bd1'], 'contains': ['192.i1', '192.l1', '192.t1', '288.dy1', '288.dz1', '288.ea1', '288.eb1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [5713, 22752, 10368, 18582, 15628, 12096], 'label': '31104.fx.96.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bd1', 'old_label': '96.bb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bb1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
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id: 186248155
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '96.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1', '48.a1'], 'contains': ['192.m1', '192.r1', '192.s1', '288.ec1', '288.ed1', '288.ef1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [1, 12384, 4032, 15588, 10924, 12096], 'label': '31104.fx.96.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.a1', 'old_label': '96.bc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bc1', 'subgroup_fusion': None, 'weyl_group': '324.124'}
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id: 186248156
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': ['288.da1', '288.de1', '288.df1', '288.ef1', '288.dz1', '288.ea1', '288.dq1', '288.ds1'], 'conjugacy_class_count': 2, 'contained_in': ['36.b1', '36.bv1', '36.bw1', '36.bx1', '54.t1', '54.bu1', '54.bv1'], 'contains': ['216.a1', '324.dn1', '324.do1', '432.mp1'], 'core': '108.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [17371, 2592, 18576, 23836, 15552, 22752, 16056], 'label': '31104.fx.108.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.a1', 'normal_contained_in': ['36.b1'], 'normal_contains': ['216.a1'], 'normalizer': '1.a1', 'old_label': '108.a1', 'projective_image': '31104.fx', 'quotient_action_image': '108.17', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '108.a1', 'subgroup_fusion': None, 'weyl_group': '10368.pi'}
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id: 186248157
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '12.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.c1', '6.k1'], 'contains': ['24.p1', '36.ca1', '36.ch1', '36.ci1', '36.cl1', '192.k1'], 'core': '72.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [26047, 15552, 10368, 16056, 5712, 4540, 18144, 18576, 22752], 'label': '31104.fx.12.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1', 'old_label': '12.p1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.p1', 'subgroup_fusion': None, 'weyl_group': '1728.46101'}
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id: 186248158
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.c1', '54.d1'], 'contains': ['216.k1', '216.l1', '216.p1', '216.y1', '216.bg1', '216.bi1', '216.bo1', '216.hq1', '216.ht1', '216.hw1', '216.ib1', '216.ie1', '216.io1', '216.ja1', '216.jo1', '324.a1', '324.c1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 12096, 18576, 6, 22752, 36, 18648], 'label': '31104.fx.108.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '108.b1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.b1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186248159
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.d1', '54.d1'], 'contains': ['216.k1', '216.l1', '216.r1', '216.z1', '216.bh1', '216.bj1', '216.bp1', '216.hr1', '216.hu1', '216.hx1', '216.ic1', '216.if1', '216.ip1', '216.jb1', '216.jp1', '324.b1', '324.d1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [8305, 12096, 18576, 6, 22752, 36, 18648], 'label': '31104.fx.108.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '108.c1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.c1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186248160
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1', '54.e1'], 'contains': ['216.n1', '216.o1', '216.bb1', '216.bk1', '216.bm1', '216.hs1', '216.hy1', '216.ia1', '216.ik1', '216.je1', '216.jk1', '324.c1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [5713, 22752, 18576, 24198, 10368, 36, 18648], 'label': '31104.fx.108.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '108.d1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.d1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186248161
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.d1', '54.e1'], 'contains': ['216.n1', '216.t1', '216.bf1', '216.bl1', '216.bn1', '216.hv1', '216.hz1', '216.id1', '216.il1', '216.jf1', '216.jl1', '324.d1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [8305, 22752, 18576, 24198, 10368, 36, 18648], 'label': '31104.fx.108.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '108.e1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.e1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186248162
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.e1', '54.d1'], 'contains': ['216.y1', '216.ba1', '216.bc1', '216.bg1', '216.bj1', '216.bp1', '216.bu1', '216.ig1', '216.ii1', '216.iq1', '216.it1', '216.iw1', '216.iy1', '216.jh1', '216.jm1', '324.e1', '324.g1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [8305, 12096, 18576, 6, 10368, 2628, 18648], 'label': '31104.fx.108.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '108.f1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.f1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
-
id: 186248163
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.f1', '54.d1'], 'contains': ['216.z1', '216.ba1', '216.bc1', '216.bh1', '216.bi1', '216.bo1', '216.ch1', '216.ih1', '216.ij1', '216.ir1', '216.iu1', '216.ix1', '216.iz1', '216.ji1', '216.jn1', '324.f1', '324.h1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 12096, 18576, 6, 22752, 2628, 18648], 'label': '31104.fx.108.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '108.g1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.g1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
-
id: 186248164
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.e1', '54.e1'], 'contains': ['216.bb1', '216.be1', '216.bl1', '216.bn1', '216.br1', '216.im1', '216.is1', '216.jc1', '216.jg1', '324.g1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [8305, 22752, 18576, 24198, 10368, 2628, 18648], 'label': '31104.fx.108.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '108.h1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.h1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
-
id: 186248165
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.f1', '54.e1'], 'contains': ['216.be1', '216.bf1', '216.bk1', '216.bm1', '216.cj1', '216.in1', '216.iv1', '216.jd1', '216.jj1', '324.h1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [5713, 22752, 18576, 24198, 10368, 2628, 18648], 'label': '31104.fx.108.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '108.i1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.i1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
-
id: 186248166
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.g1', '54.a1', '54.d1', '54.ba1'], 'contains': ['216.k1', '216.ba1', '216.cp1', '216.ct1', '216.da1', '216.jx1', '216.jy1', '216.ki1', '216.kn1', '216.kt1', '216.me1', '324.i1', '324.j1', '324.k1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [6, 12096, 16056, 36, 22752, 18576, 18144], 'label': '31104.fx.108.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '108.j1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.j1', 'subgroup_fusion': None, 'weyl_group': '288.977'}
-
id: 186248167
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.g1', '54.bb1'], 'contains': ['216.m1', '216.bd1', '216.co1', '216.cu1', '216.cx1', '216.ka1', '216.kc1', '216.kk1', '216.kw1', '216.lj1', '216.lv1', '324.k1', '324.l1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [6, 12096, 16056, 36, 10368, 18144, 18576], 'label': '31104.fx.108.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bb1', 'old_label': '108.k1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.k1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186248168
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': ['15552.c1', '15552.h1', '15552.g1', '15552.f1', '15552.e1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.b1', '4.e1', '6.b1', '6.l1', '32.e1'], 'core': '2.d1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 18576, 5712, 22752, 18144, 12138, 76, 16056, 10368, 15552, 12096], 'label': '31104.fx.2.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.b1', '4.e1', '6.b1'], 'normalizer': '1.a1', 'old_label': '2.d1', 'projective_image': '31104.fx', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.d1', 'subgroup_fusion': None, 'weyl_group': '31104.fx'}
-
id: 186248169
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '12.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1', '6.f1'], 'contains': ['24.i1', '24.l1', '24.n1', '36.cm1', '36.cn1', '36.cp1', '36.cu1', '48.i1'], 'core': '72.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [10405, 18144, 12940, 1728, 18576, 15552, 18216, 12384, 10368], 'label': '31104.fx.12.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '12.q1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.q1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
-
id: 186248170
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.g1', '54.b1', '54.d1', '54.bb1'], 'contains': ['216.l1', '216.bc1', '216.cp1', '216.cv1', '216.cy1', '216.jz1', '216.kc1', '216.kj1', '216.kv1', '216.lj2', '216.lu1', '324.j1', '324.l1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [6, 12096, 18576, 36, 10368, 16056, 2592], 'label': '31104.fx.108.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '108.l1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.l1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
-
id: 186248171
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.g1', '54.c1', '54.e1', '54.bc1'], 'contains': ['216.n1', '216.be1', '216.cq1', '216.cw1', '216.cz1', '216.kb1', '216.kd1', '216.kl1', '216.kx1', '216.lk1', '216.lw1', '324.i1', '324.l1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [24198, 22752, 16056, 36, 10368, 18576, 18144], 'label': '31104.fx.108.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '108.m1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.m1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
-
id: 186248172
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.h1', '54.e1', '54.f1', '54.bd1'], 'contains': ['216.o1', '216.t1', '216.br1', '216.cj1', '216.cq1', '216.db1', '216.dl1', '216.ke1', '216.mg1', '324.m1', '324.n1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [1, 22752, 2592, 36, 10368, 18576, 15552], 'label': '31104.fx.108.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '108.n1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.n1', 'subgroup_fusion': None, 'weyl_group': '288.977'}
-
id: 186248173
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.h1', '54.d1', '54.g1', '54.be1'], 'contains': ['216.p1', '216.r1', '216.bu1', '216.ch1', '216.cp1', '216.dc1', '216.dj1', '216.kf1', '216.kg1', '216.mh1', '216.mi1', '324.m1', '324.o1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [20737, 1728, 2592, 36, 22752, 18576, 15552], 'label': '31104.fx.108.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '108.o1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.o1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
-
id: 186248174
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.h1', '54.bf1'], 'contains': ['216.q1', '216.v1', '216.bv1', '216.ci1', '216.cr1', '216.dd1', '216.dk1', '216.kh1', '216.mj1', '324.n1', '324.o1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [20737, 1728, 2592, 36, 12384, 18576, 15552], 'label': '31104.fx.108.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '108.p1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.p1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186248175
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.i1', '54.b1', '54.g1', '54.ba1'], 'contains': ['216.cp1', '216.dm1', '216.ds1', '216.ki1', '216.mk1', '324.p1', '324.t1', '324.u1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [15558, 12096, 16056, 36, 22752, 18144, 2664], 'label': '31104.fx.108.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '108.q1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.q1', 'subgroup_fusion': None, 'weyl_group': '288.977'}
-
id: 186248176
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.i1', '54.bb1'], 'contains': ['216.co1', '216.dn1', '216.dq1', '216.kj1', '216.kk1', '216.ml1', '216.mm1', '324.q1', '324.u1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [2598, 12096, 18576, 36, 10368, 18144, 16056], 'label': '31104.fx.108.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bb1', 'old_label': '108.r1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.r1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186248177
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.i1', '54.a1', '54.g1', '54.bb1'], 'contains': ['216.cp1', '216.do1', '216.dr1', '216.kk1', '216.mm2', '324.q1', '324.t1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [15558, 12096, 18576, 36, 10368, 2592, 2664], 'label': '31104.fx.108.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '108.s1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.s1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
-
id: 186248178
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.j1', '54.a1', '54.b1', '54.be1'], 'contains': ['216.s1', '216.ck1', '216.cp1', '216.dp1', '216.dt1', '324.r1', '324.v1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [5689, 1728, 2592, 36, 22752, 18576, 15552], 'label': '31104.fx.108.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '108.t1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.t1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
-
id: 186248179
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.i1', '54.c1', '54.f1', '54.bc1'], 'contains': ['216.cq1', '216.du1', '216.dw1', '216.kl1', '216.mn1', '324.p1', '324.q1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [8646, 22752, 16056, 36, 10368, 18144, 2664], 'label': '31104.fx.108.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '108.u1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.u1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
-
id: 186248180
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '12.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.d1', '6.g1', '6.h1', '6.i1'], 'contains': ['24.a1', '36.cm1', '36.co1', '36.cq1', '36.cr1', '48.k1', '48.ba1'], 'core': '24.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [10405, 15552, 10368, 16056, 22752, 1728, 2592, 432, 16080], 'label': '31104.fx.12.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.r1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.r1', 'subgroup_fusion': None, 'weyl_group': '1152.155790'}
-
id: 186248181
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.j1', '54.c1', '54.bd1'], 'contains': ['216.u1', '216.cl1', '216.cq1', '216.dv1', '216.dx1', '324.r1', '324.s1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [16057, 22752, 2592, 36, 10368, 18576, 15552], 'label': '31104.fx.108.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '108.v1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.v1', 'subgroup_fusion': None, 'weyl_group': '288.977'}
-
id: 186248182
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.j1', '54.bf1'], 'contains': ['216.w1', '216.x1', '216.cm1', '216.cn1', '216.cr1', '216.dy1', '216.dz1', '324.s1', '324.v1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [5689, 1728, 15552, 36, 12384, 18576, 2592], 'label': '31104.fx.108.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '108.w1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.w1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186248183
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.k1', '54.d1', '54.h1', '54.bg1'], 'contains': ['216.y1', '216.z1', '216.ct1', '216.cy1', '216.dc1', '216.km1', '216.ko1', '216.kq1', '216.lr1', '324.w1', '324.x1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [26485, 18576, 22752, 12138, 12096, 16056, 2592], 'label': '31104.fx.108.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '108.x1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.x1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
-
id: 186248184
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.l1', '54.h1', '54.k1', '54.ba1'], 'contains': ['216.ct1', '216.df1', '216.ds1', '216.kt1', '216.mk1', '324.y1', '324.z1', '324.ba1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [15558, 12096, 16056, 15588, 22752, 18144, 2664], 'label': '31104.fx.108.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '108.y1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.y1', 'subgroup_fusion': None, 'weyl_group': '288.977'}
-
id: 186248185
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.m1', '54.a1', '54.k1', '54.bg1'], 'contains': ['216.ct1', '216.dp1', '216.dr1', '324.bb1', '324.bd1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [10933, 18576, 15984, 12138, 12096, 22752, 18648], 'label': '31104.fx.108.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '108.z1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.z1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
-
id: 186248186
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.n1', '54.a1', '54.h1', '54.bp1'], 'contains': ['216.ct1', '216.do1', '216.dt1', '324.bc1', '324.be1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [21265, 18576, 15984, 27690, 10368, 12096, 18648], 'label': '31104.fx.108.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '108.ba1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ba1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
-
id: 186248187
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.k1', '54.e1', '54.i1', '54.bk1'], 'contains': ['216.bb1', '216.bf1', '216.cw1', '216.cz1', '216.db1', '216.ky1', '216.la1', '216.lf1', '216.lq1', '324.w1', '324.bg1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7477, 18576, 10368, 6, 22752, 16056, 2592], 'label': '31104.fx.108.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '108.bb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bb1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
-
id: 186248188
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.k1', '54.d1', '54.j1', '54.bm1'], 'contains': ['216.bg1', '216.bh1', '216.cv1', '216.da1', '216.dc1', '216.kz1', '216.lb1', '216.lg1', '216.lx1', '324.x1', '324.bg1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [26485, 12096, 18576, 12138, 10368, 16056, 2592], 'label': '31104.fx.108.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '108.bc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bc1', 'subgroup_fusion': None, 'weyl_group': '576.7160'}
-
id: 186248189
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.l1', '54.bb1'], 'contains': ['216.cu1', '216.de1', '216.dq1', '216.lj1', '216.lj2', '216.mm1', '216.mm2', '324.ba1', '324.bh1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [2598, 12096, 18576, 2628, 10368, 18144, 16056], 'label': '31104.fx.108.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bb1', 'old_label': '108.bd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bd1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186248190
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.l1', '54.j1', '54.k1', '54.bb1'], 'contains': ['216.cv1', '216.df1', '216.dr1', '216.lj1', '216.ml1', '324.z1', '324.bh1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [15558, 12096, 18576, 15588, 10368, 2592, 2664], 'label': '31104.fx.108.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '108.be1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.be1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
-
id: 186248191
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '12.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1'], 'contains': ['24.o1', '36.cn1', '36.cp1', '36.cq1', '36.cv1', '48.l1', '48.m1'], 'core': '216.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [10405, 15552, 12384, 15624, 10368, 9168, 18144, 15984, 24268], 'label': '31104.fx.12.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1', 'old_label': '12.s1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.s1', 'subgroup_fusion': None, 'weyl_group': '288.1026'}
-
id: 186248192
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.l1', '54.i1', '54.l1', '54.bc1'], 'contains': ['216.cw1', '216.dg1', '216.dw1', '216.lk1', '216.mn1', '324.y1', '324.bh1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [8646, 22752, 16056, 15588, 10368, 18144, 2664], 'label': '31104.fx.108.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '108.bf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bf1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
-
id: 186248193
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.m1', '54.b1', '54.k1', '54.bm1'], 'contains': ['216.cv1', '216.dp1', '216.ds1', '324.bd1', '324.bi1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [10933, 12096, 18576, 12138, 10368, 18648, 15984], 'label': '31104.fx.108.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '108.bg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bg1', 'subgroup_fusion': None, 'weyl_group': '576.7160'}
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id: 186248194
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.n1', '54.b1', '54.j1', '54.bp1'], 'contains': ['216.cv1', '216.dm1', '216.dt1', '324.be1', '324.bj1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [21265, 18576, 15984, 12138, 10368, 12096, 18648], 'label': '31104.fx.108.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '108.bh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bh1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
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id: 186248195
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.m1', '54.c1', '54.l1', '54.bk1'], 'contains': ['216.cw1', '216.dv1', '216.dw1', '324.bb1', '324.bi1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [23029, 18576, 15984, 15558, 22752, 10368, 18648], 'label': '31104.fx.108.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '108.bi1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bi1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
-
id: 186248196
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.n1', '54.c1', '54.i1', '54.br1'], 'contains': ['216.cw1', '216.du1', '216.dx1', '324.bc1', '324.bj1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [21265, 22752, 18576, 27690, 10368, 18648, 15984], 'label': '31104.fx.108.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '108.bj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bj1', 'subgroup_fusion': None, 'weyl_group': '576.7160'}
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id: 186248197
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.o1', '54.d1', '54.k1', '54.bp1'], 'contains': ['216.bi1', '216.bj1', '216.ct1', '216.cv1', '216.dj1', '216.kp1', '216.lc1', '216.le1', '216.ll1', '324.bf1', '324.bk1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [5713, 18576, 12096, 12138, 10368, 16056, 2592], 'label': '31104.fx.108.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '108.bk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bk1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
-
id: 186248198
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.o1', '54.e1', '54.l1', '54.br1'], 'contains': ['216.bk1', '216.bl1', '216.cw1', '216.dl1', '216.ld1', '216.lo1', '324.bk1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [5713, 22752, 18576, 12138, 10368, 16056, 2592], 'label': '31104.fx.108.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '108.bl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bl1', 'subgroup_fusion': None, 'weyl_group': '576.7160'}
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id: 186248199
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.p1', '54.bb1'], 'contains': ['216.cx1', '216.de1', '216.dn1', '216.lu1', '216.lv1', '216.ml1', '216.mm2', '324.bl1', '324.bq1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [6, 12096, 18576, 2628, 10368, 18144, 16056], 'label': '31104.fx.108.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bb1', 'old_label': '108.bm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bm1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186248200
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.p1', '54.h1', '54.n1', '54.bb1'], 'contains': ['216.cy1', '216.df1', '216.do1', '216.lv1', '216.mm1', '324.bl1', '324.bp1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [6, 12096, 18576, 15588, 10368, 2592, 2664], 'label': '31104.fx.108.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '108.bn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bn1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
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id: 186248201
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.p1', '54.i1', '54.m1', '54.bc1'], 'contains': ['216.cz1', '216.dg1', '216.du1', '216.lw1', '216.mn1', '324.bl1', '324.bo1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [24198, 22752, 16056, 15588, 10368, 18144, 2664], 'label': '31104.fx.108.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '108.bo1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bo1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
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id: 186248202
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '12.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1', '6.d1', '6.j1'], 'contains': ['24.b1', '36.cn1', '36.co1', '36.cs1', '36.cw1', '48.n1'], 'core': '24.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [10405, 15552, 16080, 15624, 22752, 12460, 18144, 15984, 10368], 'label': '31104.fx.12.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.t1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.t1', 'subgroup_fusion': None, 'weyl_group': '1152.157852'}
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id: 186248203
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.q1', '54.b1', '54.n1', '54.bg1'], 'contains': ['216.cy1', '216.dm1', '216.dp1', '324.bm1', '324.bt1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [10933, 18576, 15984, 27690, 12096, 22752, 18648], 'label': '31104.fx.108.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '108.bp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bp1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
-
id: 186248204
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.r1', '54.b1', '54.h1', '54.ce1'], 'contains': ['216.cy1', '216.ds1', '216.dt1', '324.bn1', '324.bu1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [21265, 12096, 18576, 6, 10368, 18648, 15984], 'label': '31104.fx.108.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '108.bq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bq1', 'subgroup_fusion': None, 'weyl_group': '576.7160'}
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id: 186248205
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.q1', '54.c1', '54.m1', '54.bk1'], 'contains': ['216.cz1', '216.du1', '216.dv1', '324.bm1', '324.br1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [23029, 18576, 15984, 6, 22752, 10368, 18648], 'label': '31104.fx.108.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '108.br1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.br1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
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id: 186248206
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.r1', '54.c1', '54.i1', '54.by1'], 'contains': ['216.cz1', '216.dw1', '216.dx1', '324.bn1', '324.bs1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [21265, 22752, 18576, 15558, 10368, 18648, 15984], 'label': '31104.fx.108.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '108.bs1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bs1', 'subgroup_fusion': None, 'weyl_group': '576.7160'}
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id: 186248207
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.s1', '54.e1', '54.m1', '54.by1'], 'contains': ['216.bm1', '216.bn1', '216.cz1', '216.dl1', '216.lt1', '216.mb1', '324.bv1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [5713, 22752, 18576, 6, 10368, 16056, 2592], 'label': '31104.fx.108.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '108.bt1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bt1', 'subgroup_fusion': None, 'weyl_group': '576.7160'}
-
id: 186248208
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.p1', '54.j1', '54.n1', '54.ba1'], 'contains': ['216.da1', '216.df1', '216.dm1', '216.me1', '216.mk1', '324.bo1', '324.bp1', '324.bq1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [6, 12096, 16056, 15588, 22752, 18144, 2664], 'label': '31104.fx.108.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '108.bu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bu1', 'subgroup_fusion': None, 'weyl_group': '288.977'}
-
id: 186248209
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.q1', '54.a1', '54.n1', '54.bm1'], 'contains': ['216.da1', '216.do1', '216.dp1', '324.br1', '324.bt1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [10933, 12096, 18576, 27690, 10368, 18648, 15984], 'label': '31104.fx.108.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '108.bv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bv1', 'subgroup_fusion': None, 'weyl_group': '576.7160'}
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id: 186248210
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.r1', '54.a1', '54.j1', '54.ce1'], 'contains': ['216.da1', '216.dr1', '216.dt1', '324.bs1', '324.bu1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [21265, 12096, 18576, 15558, 10368, 18648, 15984], 'label': '31104.fx.108.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '108.bw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bw1', 'subgroup_fusion': None, 'weyl_group': '576.7160'}
-
id: 186248211
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.s1', '54.d1', '54.n1', '54.ce1'], 'contains': ['216.bo1', '216.bp1', '216.cy1', '216.da1', '216.dj1', '216.ls1', '216.ly1', '216.md1', '216.mf1', '324.bv1', '324.bw1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [5713, 12096, 18576, 6, 10368, 16056, 2592], 'label': '31104.fx.108.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '108.bx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bx1', 'subgroup_fusion': None, 'weyl_group': '576.7160'}
-
id: 186248212
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.t1', '54.i1', '54.bd1'], 'contains': ['216.bq1', '216.cc1', '216.db1', '216.dg1', '216.dx1', '324.bx1', '324.by1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [16057, 22752, 2592, 16092, 10368, 18576, 15552], 'label': '31104.fx.108.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '108.by1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.by1', 'subgroup_fusion': None, 'weyl_group': '288.977'}
-
id: 186248213
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '12.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.d1', '6.k1'], 'contains': ['24.p1', '36.co1', '36.cp1', '36.cq1', '36.ct1', '48.o1'], 'core': '72.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [10405, 15552, 10368, 15624, 22752, 16080, 18144, 15984, 24268], 'label': '31104.fx.12.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1', 'old_label': '12.u1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.u1', 'subgroup_fusion': None, 'weyl_group': '576.8654'}
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id: 186248214
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.u1', '54.f1', '54.i1', '54.bk1'], 'contains': ['216.db1', '216.du1', '216.dw1', '324.bz1', '324.ca1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7477, 18576, 15984, 15558, 22752, 10368, 18648], 'label': '31104.fx.108.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '108.bz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bz1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
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id: 186248215
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.t1', '54.h1', '54.j1', '54.be1'], 'contains': ['216.bs1', '216.ca1', '216.dc1', '216.df1', '216.dt1', '324.bx1', '324.cb1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [16057, 1728, 2592, 16092, 10368, 18576, 15552], 'label': '31104.fx.108.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '108.ca1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ca1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
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id: 186248216
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.t1', '54.bf1'], 'contains': ['216.bt1', '216.bt2', '216.ce1', '216.ce2', '216.dd1', '216.dh1', '216.dz1', '324.by1', '324.cb1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [5689, 1728, 15552, 16092, 12384, 18576, 2592], 'label': '31104.fx.108.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '108.cb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cb1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186248217
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.u1', '54.g1', '54.j1', '54.bg1'], 'contains': ['216.dc1', '216.dm1', '216.dr1', '324.bz1', '324.cc1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [26485, 18576, 15984, 27690, 12096, 22752, 18648], 'label': '31104.fx.108.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '108.cc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cc1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
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id: 186248218
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.u1', '54.g1', '54.h1', '54.bm1'], 'contains': ['216.dc1', '216.do1', '216.ds1', '324.ca1', '324.cc1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [26485, 12096, 18576, 27690, 10368, 18648, 15984], 'label': '31104.fx.108.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '108.cd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cd1', 'subgroup_fusion': None, 'weyl_group': '576.7160'}
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id: 186248219
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.v1', '54.k1', '54.n1', '54.be1'], 'contains': ['216.bw1', '216.cb1', '216.df1', '216.dj1', '216.dp1', '324.cd1', '324.ce1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [20737, 1728, 2592, 16092, 22752, 18576, 15552], 'label': '31104.fx.108.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '108.ce1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ce1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
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id: 186248220
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.v1', '54.bf1'], 'contains': ['216.bx1', '216.by1', '216.cf1', '216.cg1', '216.dh1', '216.dk1', '216.dy1', '324.cd1', '324.cf1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [20737, 1728, 15552, 16092, 12384, 18576, 2592], 'label': '31104.fx.108.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '108.cf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cf1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186248221
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.v1', '54.l1', '54.m1', '54.bd1'], 'contains': ['216.bz1', '216.cd1', '216.dg1', '216.dl1', '216.dv1', '324.ce1', '324.cf1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [1, 22752, 2592, 16092, 10368, 18576, 15552], 'label': '31104.fx.108.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '108.cg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cg1', 'subgroup_fusion': None, 'weyl_group': '288.977'}
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id: 186248222
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.w1', '54.g1', '54.n1', '54.bp1'], 'contains': ['216.dj1', '216.dm1', '216.do1', '324.cg1', '324.ci1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [5713, 18576, 15984, 27690, 10368, 12096, 18648], 'label': '31104.fx.108.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '108.ch1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ch1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
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id: 186248223
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.x1', '54.g1', '54.k1', '54.ce1'], 'contains': ['216.dj1', '216.dr1', '216.ds1', '324.ch1', '324.cj1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [5713, 12096, 18576, 15558, 10368, 18648, 15984], 'label': '31104.fx.108.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '108.ci1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ci1', 'subgroup_fusion': None, 'weyl_group': '576.7160'}
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id: 186248224
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '12.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1', '6.f1'], 'contains': ['24.k1', '24.m1', '24.n1', '36.cz1', '36.da1', '36.db1', '36.de1', '48.q1'], 'core': '72.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1, 18144, 10924, 12384, 18576, 15552, 18216, 10368, 12096], 'label': '31104.fx.12.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '12.v1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.v1', 'subgroup_fusion': None, 'weyl_group': None}
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id: 186248225
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.w1', '54.f1', '54.m1', '54.br1'], 'contains': ['216.dl1', '216.du1', '324.ci1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [5713, 22752, 18576, 27690, 10368, 18648, 15984], 'label': '31104.fx.108.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '108.cj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cj1', 'subgroup_fusion': None, 'weyl_group': '576.7160'}
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id: 186248226
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.x1', '54.f1', '54.l1', '54.by1'], 'contains': ['216.dl1', '216.dw1', '324.cj1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [5713, 22752, 18576, 15558, 10368, 18648, 15984], 'label': '31104.fx.108.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '108.ck1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ck1', 'subgroup_fusion': None, 'weyl_group': '576.7160'}
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id: 186248227
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.y1', '54.u1'], 'contains': ['216.ec1', '216.eq1', '216.ew1', '216.fg1', '216.fz1', '324.ck1', '324.cm1', '432.bd1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [20737, 72, 22752, 36, 18144, 2664, 21292], 'label': '31104.fx.108.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.u1', 'old_label': '108.cl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cl1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
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id: 186248228
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.y1', '54.x1'], 'contains': ['216.eh1', '216.er1', '216.ex1', '216.fk1', '216.gb1', '324.ck1', '324.co1', '432.be1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [20737, 72, 2016, 36, 18144, 2664, 10924], 'label': '31104.fx.108.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '108.cm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cm1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
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id: 186248229
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.y1', '36.z1', '54.y1'], 'contains': ['216.ei1', '216.es1', '216.ey1', '216.fl1', '216.gc1', '324.ck1', '324.cn1', '432.bf1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [20737, 72, 12384, 36, 18144, 2664, 556], 'label': '31104.fx.108.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.y1', 'old_label': '108.cn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cn1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
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id: 186248230
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.ba1', '54.u1'], 'contains': ['216.ew1', '216.gg1', '216.gh1', '324.cl1', '324.cq1', '432.bg1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [8209, 18216, 22752, 36, 18144, 2592, 8332], 'label': '31104.fx.108.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.u1', 'old_label': '108.co1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.co1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
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id: 186248231
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ba1', '54.x1'], 'contains': ['216.ex1', '216.gp1', '216.gq1', '324.cl1', '324.cs1', '432.bh1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [8209, 18216, 2016, 36, 18144, 2592, 29068], 'label': '31104.fx.108.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '108.cp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cp1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
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id: 186248232
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ba1', '36.bb1', '54.y1'], 'contains': ['216.ey1', '216.gr1', '216.gs1', '324.cl1', '324.cr1', '432.bi1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [8209, 18216, 12384, 36, 18144, 2592, 18700], 'label': '31104.fx.108.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.y1', 'old_label': '108.cq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cq1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
-
id: 186248233
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.y1', '36.bc1', '54.bd1'], 'contains': ['216.c1', '216.g1', '216.o1', '216.u1', '216.bq1', '216.bz1', '216.el1', '216.ep1', '216.fa1', '216.fe1', '216.ga1', '324.cm1', '324.cn1', '324.co1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1, 22752, 15552, 36, 10368, 16056, 2592], 'label': '31104.fx.108.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bd1', 'old_label': '108.cr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cr1', 'subgroup_fusion': None, 'weyl_group': '144.196'}
-
id: 186248234
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.bc1', '54.be1'], 'contains': ['216.d1', '216.h1', '216.p1', '216.s1', '216.bs1', '216.bw1', '216.em1', '216.et1', '216.ez1', '216.ff1', '216.fw1', '324.cm1', '324.cp1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [20737, 1728, 15552, 36, 22752, 16056, 2592], 'label': '31104.fx.108.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.be1', 'old_label': '108.cs1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cs1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186248235
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '12.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.e1', '6.g1', '6.l1', '6.n1'], 'contains': ['24.a1', '36.cx1', '36.cy1', '36.cz1', '36.df1', '48.s1', '48.bb1'], 'core': '24.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1, 15552, 10368, 16056, 12096, 22752, 2592, 432, 5712], 'label': '31104.fx.12.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.w1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.w1', 'subgroup_fusion': None, 'weyl_group': '10368.je'}
-
id: 186248236
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.z1', '36.bc1', '54.bf1'], 'contains': ['216.f1', '216.j1', '216.q1', '216.x1', '216.bt1', '216.by1', '216.eo1', '216.ev1', '216.fb1', '216.fi1', '216.fx1', '324.cn1', '324.cp1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [20737, 1728, 18144, 36, 12384, 2664, 15552], 'label': '31104.fx.108.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '108.ct1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ct1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186248237
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bc1', '54.bf1'], 'contains': ['216.e1', '216.i1', '216.q1', '216.w1', '216.bt2', '216.bx1', '216.en1', '216.eu1', '216.fd1', '216.fj1', '216.fy1', '324.co1', '324.cp1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [20737, 1728, 15552, 36, 12384, 16056, 18144], 'label': '31104.fx.108.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '108.cu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cu1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186248238
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.bd1', '54.be1'], 'contains': ['216.r1', '216.s1', '216.ca1', '216.cb1', '216.ez1', '216.ge1', '216.gf1', '324.cq1', '324.ct1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [21169, 1728, 2592, 36, 22752, 16056, 15552], 'label': '31104.fx.108.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.be1', 'old_label': '108.cv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cv1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186248239
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ba1', '36.bd1', '54.bd1'], 'contains': ['216.t1', '216.u1', '216.cc1', '216.cd1', '216.fa1', '216.gj1', '216.gk1', '324.cq1', '324.cr1', '324.cs1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [433, 22752, 2592, 36, 10368, 16056, 15552], 'label': '31104.fx.108.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bd1', 'old_label': '108.cw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cw1', 'subgroup_fusion': None, 'weyl_group': '144.196'}
-
id: 186248240
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bb1', '36.bd1', '54.bf1'], 'contains': ['216.v1', '216.w1', '216.ce1', '216.cf1', '216.fb1', '216.gl1', '216.gn1', '324.cr1', '324.ct1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [8209, 1728, 15552, 36, 12384, 2664, 2592], 'label': '31104.fx.108.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '108.cx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cx1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186248241
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bd1', '54.bf1'], 'contains': ['216.v1', '216.x1', '216.ce2', '216.cg1', '216.fd1', '216.gm1', '216.go1', '324.cs1', '324.ct1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [8209, 1728, 15552, 36, 12384, 16056, 2592], 'label': '31104.fx.108.cy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '108.cy1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cy1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186248242
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.be1', '36.bf1', '54.bd1'], 'contains': ['216.bq1', '216.br1', '216.cd1', '216.cl1', '216.fe1', '216.fs1', '216.gk1', '324.cu1', '324.cv1', '324.cw1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [433, 22752, 2592, 468, 10368, 16056, 15552], 'label': '31104.fx.108.cz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bd1', 'old_label': '108.cz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cz1', 'subgroup_fusion': None, 'weyl_group': '144.196'}
-
id: 186248243
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.be1', '54.u1'], 'contains': ['216.fg1', '216.fo1', '216.gh1', '324.cu1', '324.cx1', '432.bu1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [8209, 18216, 22752, 18612, 18144, 2592, 8332], 'label': '31104.fx.108.da1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.u1', 'old_label': '108.da1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.da1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
-
id: 186248244
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.be1', '54.x1'], 'contains': ['216.fk1', '216.fp1', '216.gq1', '324.cw1', '324.cx1', '432.bv1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [8209, 18216, 2016, 18612, 18144, 2592, 29068], 'label': '31104.fx.108.db1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '108.db1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.db1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
-
id: 186248245
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.be1', '36.bg1', '54.y1'], 'contains': ['216.fl1', '216.fq1', '216.gs1', '324.cv1', '324.cx1', '432.bw1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [8209, 18216, 12384, 18612, 18144, 2592, 18700], 'label': '31104.fx.108.dc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.y1', 'old_label': '108.dc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dc1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
-
id: 186248246
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '12.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3.b1'], 'contains': ['24.q1', '24.r1', '24.s1', '24.t1', '24.u1', '24.v1', '24.w1', '36.di1', '36.dj1', '36.dl1', '48.bd1'], 'core': '576.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [1, 2592, 12096, 22752, 6, 5712, 18576, 10368, 36], 'label': '31104.fx.12.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.x1', 'old_label': '12.x1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.x1', 'subgroup_fusion': None, 'weyl_group': '2592.jb'}
-
id: 186248247
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.bf1', '54.be1'], 'contains': ['216.bs1', '216.bu1', '216.cb1', '216.ck1', '216.ff1', '216.fr1', '216.gf1', '324.cu1', '324.cy1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [21169, 1728, 2592, 468, 22752, 16056, 15552], 'label': '31104.fx.108.dd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.be1', 'old_label': '108.dd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dd1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186248248
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bf1', '36.bg1', '54.bf1'], 'contains': ['216.bt2', '216.bv1', '216.cg1', '216.cn1', '216.fi1', '216.ft1', '216.gn1', '324.cv1', '324.cy1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [8209, 1728, 15552, 18612, 12384, 2664, 2592], 'label': '31104.fx.108.de1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '108.de1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.de1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186248249
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bf1', '54.bf1'], 'contains': ['216.bt1', '216.bv1', '216.cf1', '216.cm1', '216.fj1', '216.fv1', '216.go1', '324.cw1', '324.cy1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [8209, 1728, 15552, 18612, 12384, 16056, 2592], 'label': '31104.fx.108.df1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '108.df1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.df1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186248250
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.bi1', '54.u1'], 'contains': ['216.fo1', '216.fz1', '216.gg1', '324.cz1', '324.db1', '432.cg1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [20737, 18216, 22752, 18612, 18144, 2592, 21292], 'label': '31104.fx.108.dg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.u1', 'old_label': '108.dg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dg1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
-
id: 186248251
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bi1', '54.x1'], 'contains': ['216.fp1', '216.gb1', '216.gp1', '324.cz1', '324.dd1', '432.ch1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [20737, 18216, 2016, 18612, 18144, 2592, 10924], 'label': '31104.fx.108.dh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '108.dh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dh1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
-
id: 186248252
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bh1', '36.bi1', '54.y1'], 'contains': ['216.fq1', '216.gc1', '216.gr1', '324.cz1', '324.dc1', '432.ci1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [20737, 18216, 12384, 18612, 18144, 2592, 556], 'label': '31104.fx.108.di1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.y1', 'old_label': '108.di1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.di1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
-
id: 186248253
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.bj1', '54.be1'], 'contains': ['216.bw1', '216.ca1', '216.ch1', '216.ck1', '216.fr1', '216.fw1', '216.ge1', '324.da1', '324.db1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [20737, 1728, 2592, 468, 22752, 16056, 15552], 'label': '31104.fx.108.dj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.be1', 'old_label': '108.dj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dj1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186248254
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bh1', '36.bj1', '54.bf1'], 'contains': ['216.bx1', '216.ce2', '216.ci1', '216.cm1', '216.ft1', '216.fx1', '216.gl1', '324.da1', '324.dc1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [20737, 1728, 15552, 18612, 12384, 2664, 2592], 'label': '31104.fx.108.dk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '108.dk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dk1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186248255
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bj1', '54.bf1'], 'contains': ['216.by1', '216.ce1', '216.ci1', '216.cn1', '216.fv1', '216.fy1', '216.gm1', '324.da1', '324.dd1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [20737, 1728, 15552, 18612, 12384, 16056, 2592], 'label': '31104.fx.108.dl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '108.dl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dl1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186248256
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bi1', '36.bj1', '54.bd1'], 'contains': ['216.bz1', '216.cc1', '216.cj1', '216.cl1', '216.fs1', '216.ga1', '216.gj1', '324.db1', '324.dc1', '324.dd1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1, 22752, 2592, 468, 10368, 16056, 15552], 'label': '31104.fx.108.dm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bd1', 'old_label': '108.dm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dm1', 'subgroup_fusion': None, 'weyl_group': '144.196'}
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id: 186248257
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '16.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '8.b1'], 'contains': ['32.a1', '48.e1', '48.f1', '48.g1', '48.h1', '64.a1'], 'core': '576.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [36, 15552, 12096, 76, 18648, 10368, 12384, 5712], 'label': '31104.fx.16.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1', 'old_label': '16.a1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.a1', 'subgroup_fusion': None, 'weyl_group': None}
-
id: 186248258
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bk1', '36.bl1', '54.o1', '54.p1'], 'contains': ['216.hl1', '324.de1', '324.df1', '432.eq1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [36, 18144, 18576, 12460, 15552, 16080, 16056], 'label': '31104.fx.108.dn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.dn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dn1', 'subgroup_fusion': None, 'weyl_group': '576.8654'}
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id: 186248259
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.bk1', '36.bn1', '54.u1'], 'contains': ['216.ew1', '216.fo1', '216.gx1', '324.de1', '324.dg1', '432.er1'], 'core': '648.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [36, 18144, 72, 18576, 22752, 15552, 21292], 'label': '31104.fx.108.do1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '108.do1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.do1', 'subgroup_fusion': None, 'weyl_group': '432.747'}
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id: 186248260
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.bk1', '36.bo1', '54.r1', '54.s1', '54.v1'], 'contains': ['216.gy1', '324.df1', '324.dg1', '432.et1', '432.lv1'], 'core': '648.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [36, 15552, 2592, 16080, 22752, 15624, 432], 'label': '31104.fx.108.dp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '108.dp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dp1', 'subgroup_fusion': None, 'weyl_group': '3456.di'}
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id: 186248261
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.bk1', '36.bm1', '36.bo1', '54.q1', '54.t1', '54.w1'], 'contains': ['216.a1', '324.df1', '324.dg1', '432.eu1', '432.lw1'], 'core': '216.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [36, 15552, 2592, 16080, 10368, 15624, 432], 'label': '31104.fx.108.dq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '108.dq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dq1', 'subgroup_fusion': None, 'weyl_group': '3456.di'}
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id: 186248262
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bl1', '36.bn1', '54.x1'], 'contains': ['216.ex1', '216.fp1', '216.hd1', '324.de1', '324.dh1', '432.ev1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [36, 18144, 72, 18576, 2016, 15552, 10924], 'label': '31104.fx.108.dr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1', 'old_label': '108.dr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dr1', 'subgroup_fusion': None, 'weyl_group': '432.747'}
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id: 186248263
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bl1', '36.bn1', '36.bp1', '54.y1'], 'contains': ['216.ey1', '216.fq1', '216.he1', '324.de1', '324.dh1', '432.ew1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [36, 18144, 72, 18576, 12384, 15552, 556], 'label': '31104.fx.108.ds1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1', 'old_label': '108.ds1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ds1', 'subgroup_fusion': None, 'weyl_group': '432.747'}
-
id: 186248264
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.bl1', '36.bo1', '54.z1'], 'contains': ['216.hf1', '324.df1', '324.dh1', '432.ez1', '432.fa1', '432.lx1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [36, 15552, 2592, 76, 12384, 2664, 18576], 'label': '31104.fx.108.dt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1', 'old_label': '108.dt1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dt1', 'subgroup_fusion': None, 'weyl_group': '1728.47859'}
-
id: 186248265
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.a1', '36.bm1', '54.ba1', '54.bb1', '54.be1'], 'contains': ['216.co1', '216.cp1', '216.de1', '216.df1', '216.ez1', '216.fr1', '216.gw1', '324.dg1', '324.di1'], 'core': '648.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [36, 12096, 15552, 16056, 10368, 18576, 18144], 'label': '31104.fx.108.du1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '108.du1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.du1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
-
id: 186248266
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.dv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1', '36.bn1', '36.bo1', '54.bc1', '54.bd1'], 'contains': ['216.b1', '216.cq1', '216.dg1', '216.fa1', '216.fs1', '324.dg1', '324.dh1'], 'core': '216.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [36, 22752, 15552, 16056, 10368, 18576, 18144], 'label': '31104.fx.108.dv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '108.dv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dv1', 'subgroup_fusion': None, 'weyl_group': '648.734'}
-
id: 186248267
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1', '36.bp1', '54.bf1'], 'contains': ['216.cr1', '216.cs1', '216.dh1', '216.di1', '216.fb1', '216.fc1', '216.fd1', '216.ft1', '216.fu1', '216.fv1', '216.hc1', '324.dh1', '324.di1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [36, 12096, 15552, 16056, 12384, 18576, 18144], 'label': '31104.fx.108.dw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.r1', 'old_label': '108.dw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dw1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
-
id: 186248268
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1', '8.b1'], 'contains': ['32.a1', '48.i1', '48.j1', '48.k1', '48.l1', '48.m1', '48.n1', '48.o1', '64.d1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [10405, 22752, 10368, 12460, 1728, 15552, 18648, 16080], 'label': '31104.fx.16.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1', 'old_label': '16.b1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1', 'subgroup_fusion': None, 'weyl_group': '432.747'}
-
id: 186248269
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.dx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.gc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.bq1', '36.bs1', '54.ba1', '54.bg1', '54.bp1'], 'contains': ['216.ct1', '216.dm1', '216.gw1', '324.dj1', '324.dk1'], 'core': '648.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [17371, 18576, 10368, 16056, 2592, 15552, 12096], 'label': '31104.fx.108.dx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '108.dx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dx1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
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id: 186248270
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.bq1', '36.br1', '36.bt1', '54.q1', '54.bh1', '54.bv1'], 'contains': ['216.a1', '324.dj1', '324.dl1', '432.mf1'], 'core': '216.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [12138, 2592, 18576, 20812, 15552, 22752, 2664], 'label': '31104.fx.108.dy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '108.dy1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dy1', 'subgroup_fusion': None, 'weyl_group': '1152.155790'}
-
id: 186248271
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.bq1', '36.bu1', '54.bi1'], 'contains': ['216.hb1', '324.dj1', '324.dm1', '432.mg1'], 'core': '648.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [17371, 2592, 15984, 29904, 15552, 10368, 15624], 'label': '31104.fx.108.dz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.u1', 'old_label': '108.dz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dz1', 'subgroup_fusion': None, 'weyl_group': '576.5512'}
-
id: 186248272
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.gc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.bs1', '36.bv1', '54.bb1', '54.bm1', '54.bp1'], 'contains': ['216.cu1', '216.cv1', '216.dn1', '216.do1', '216.gw1', '324.dk1', '324.dn1'], 'core': '648.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [12138, 18576, 16056, 18144, 10368, 15552, 12096], 'label': '31104.fx.108.ea1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '108.ea1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ea1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
-
id: 186248273
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.eb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.b1', '36.br1', '54.s1', '54.bj1', '54.bq1'], 'contains': ['216.gy1', '324.dj1', '324.do1', '432.mj1'], 'core': '648.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [12138, 18144, 432, 22752, 15552, 5712, 16056], 'label': '31104.fx.108.eb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '108.eb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.eb1', 'subgroup_fusion': None, 'weyl_group': '1152.157852'}
-
id: 186248274
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.ec1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.bt1', '36.bw1', '54.r1', '54.bn1', '54.bq1'], 'contains': ['216.gy1', '324.dl1', '324.dn1', '432.mm1'], 'core': '648.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [12138, 15552, 2592, 76, 10368, 2664, 18576], 'label': '31104.fx.108.ec1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '108.ec1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ec1', 'subgroup_fusion': None, 'weyl_group': '1152.155790'}
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id: 186248275
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.ed1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.bu1', '36.bx1', '54.bo1'], 'contains': ['216.hb2', '324.dm1', '324.dn1', '432.mn1'], 'core': '648.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [17371, 15552, 2592, 29904, 22752, 15624, 15984], 'label': '31104.fx.108.ed1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.y1', 'old_label': '108.ed1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ed1', 'subgroup_fusion': None, 'weyl_group': '576.5126'}
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id: 186248276
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.ee1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.gc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.b1', '36.bs1', '36.bt1', '36.bu1', '54.bc1', '54.bk1', '54.br1'], 'contains': ['216.b1', '216.cw1', '216.du1', '324.dj1', '324.dn1'], 'core': '216.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [12138, 18576, 16056, 18144, 10368, 15552, 22752], 'label': '31104.fx.108.ee1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '108.ee1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ee1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
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id: 186248277
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.ef1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.q1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.br1', '36.bw1', '54.o1', '54.bl1', '54.bs1'], 'contains': ['216.hl1', '324.dl1', '324.do1', '1728.bk1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [12138, 2592, 15984, 20812, 15552, 5712, 15624], 'label': '31104.fx.108.ef1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '108.ef1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ef1', 'subgroup_fusion': None, 'weyl_group': '576.8654'}
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id: 186248278
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.eg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.br1', '36.bw1', '54.bt1'], 'contains': ['216.ho1', '324.dl1', '324.do1', '1728.bl1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [12138, 2592, 15984, 12460, 15552, 5712, 15624], 'label': '31104.fx.108.eg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bf1', 'old_label': '108.eg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.eg1', 'subgroup_fusion': None, 'weyl_group': '576.8654'}
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id: 186248279
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '2.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': ['15552.c1', '15552.h1', '15552.g1', '15552.f1', '15552.d1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.c1', '4.e1', '6.m1', '6.n1', '32.f1'], 'core': '2.e1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 18576, 12096, 22752, 18144, 6, 5712, 16056, 10368, 15552, 76], 'label': '31104.fx.2.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.c1', '4.e1'], 'normalizer': '1.a1', 'old_label': '2.e1', 'projective_image': '31104.fx', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.e1', 'subgroup_fusion': None, 'weyl_group': '31104.fx'}
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id: 186248280
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '16.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1', '8.b1'], 'contains': ['32.a1', '48.q1', '48.r1', '48.s1', '48.t1', '64.e1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [1, 22752, 10368, 12096, 5712, 15552, 18648, 76], 'label': '31104.fx.16.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1', 'old_label': '16.c1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.c1', 'subgroup_fusion': None, 'weyl_group': None}
-
id: 186248281
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.eh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.by1', '36.bz1', '36.ca1', '54.r1', '54.bj1', '54.cd1'], 'contains': ['216.gy1', '324.dp1', '324.dq1', '324.dr1', '432.mq1'], 'core': '648.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [6, 2592, 18576, 76, 15552, 10368, 2664], 'label': '31104.fx.108.eh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '108.eh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.eh1', 'subgroup_fusion': None, 'weyl_group': '384.17948'}
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id: 186248282
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.ei1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ep1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.cb1', '36.cd1', '36.cj1', '54.bb1', '54.bg1', '54.ce1'], 'contains': ['216.cx1', '216.cy1', '216.dq1', '216.dr1', '216.gw1', '324.dp1', '324.dt1'], 'core': '648.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [6, 18576, 16056, 18144, 12096, 15552, 10368], 'label': '31104.fx.108.ei1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '108.ei1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ei1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186248283
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.bz1', '36.cb1', '36.ck1', '54.t1', '54.bh1', '54.bw1'], 'contains': ['216.a1', '324.dp1', '324.du1', '432.mt1'], 'core': '216.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [26047, 2592, 18576, 22752, 15552, 23836, 16056], 'label': '31104.fx.108.ej1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '108.ej1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ej1', 'subgroup_fusion': None, 'weyl_group': '1152.157852'}
-
id: 186248284
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.ca1', '36.cc1', '36.cg1', '36.ch1', '54.q1', '54.bu1', '54.bw1'], 'contains': ['216.a1', '324.dq1', '324.ds1', '432.my1'], 'core': '216.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [6, 15552, 2592, 20812, 22752, 2664, 18576], 'label': '31104.fx.108.ek1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '108.ek1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ek1', 'subgroup_fusion': None, 'weyl_group': '1152.155790'}
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id: 186248285
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.el1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.by1', '36.cd1', '36.ck1', '54.bx1'], 'contains': ['216.gz1', '324.dp1', '324.dv1', '432.mu1'], 'core': '648.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [6, 18144, 432, 10368, 15552, 28464, 16056], 'label': '31104.fx.108.el1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bh1', 'old_label': '108.el1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.el1', 'subgroup_fusion': None, 'weyl_group': '576.8654'}
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id: 186248286
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.em1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.ca1', '36.ce1', '36.cf1', '36.ci1', '54.bx1'], 'contains': ['216.gz1', '324.dr1', '324.ds1', '432.mz1'], 'core': '648.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [6, 15552, 2592, 76, 22752, 2664, 18576], 'label': '31104.fx.108.em1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '108.em1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.em1', 'subgroup_fusion': None, 'weyl_group': '576.5126'}
-
id: 186248287
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.en1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.cb1', '36.cd1', '36.cl1', '54.bi1'], 'contains': ['216.hb1', '324.dp1', '324.dw1', '432.mv1', '432.mv2'], 'core': '648.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [6, 18144, 432, 10368, 15552, 19536, 16056], 'label': '31104.fx.108.en1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bi1', 'old_label': '108.en1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.en1', 'subgroup_fusion': None, 'weyl_group': '192.955'}
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id: 186248288
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.eo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ep1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.ca1', '36.cj1', '36.ck1', '36.cl1', '54.bc1', '54.bk1', '54.by1'], 'contains': ['216.b1', '216.cz1', '216.dw1', '324.dp1', '324.ds1'], 'core': '216.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [26047, 2592, 18576, 16056, 10368, 15552, 22752], 'label': '31104.fx.108.eo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '108.eo1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.eo1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
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id: 186248289
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.ep1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.q1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.bz1', '36.cg1', '54.o1', '54.bl1', '54.bz1'], 'contains': ['216.hl1', '324.dq1', '324.du1', '1728.bv1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [6, 2592, 15984, 20812, 15552, 5712, 15624], 'label': '31104.fx.108.ep1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '108.ep1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ep1', 'subgroup_fusion': None, 'weyl_group': '576.8654'}
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id: 186248290
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.eq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.by1', '36.cf1', '54.ca1'], 'contains': ['216.hm1', '324.dr1', '324.dv1', '1728.bw1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [6, 2592, 15984, 76, 15552, 28464, 15624], 'label': '31104.fx.108.eq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bh1', 'old_label': '108.eq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.eq1', 'subgroup_fusion': None, 'weyl_group': '576.8654'}
-
id: 186248291
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '16.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['32.b1', '32.c1', '32.d1', '32.e1', '32.f1', '48.bc1', '48.bd1'], 'core': '576.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [1, 5712, 12096, 6, 18580, 10368, 22752, 36], 'label': '31104.fx.16.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.d1', 'old_label': '16.d1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.d1', 'subgroup_fusion': None, 'weyl_group': '1944.2342'}
-
id: 186248292
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.er1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.by1', '36.cg1', '54.cb1'], 'contains': ['216.hn1', '324.dq1', '324.dv1', '1728.bx1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [26047, 18144, 18576, 5712, 15552, 3100, 16056], 'label': '31104.fx.108.er1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bh1', 'old_label': '108.er1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.er1', 'subgroup_fusion': None, 'weyl_group': '576.8654'}
-
id: 186248293
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.es1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.bz1', '36.cf1', '54.cb1'], 'contains': ['216.hn1', '324.dr1', '324.du1', '1728.by1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [6, 2592, 15984, 76, 15552, 5712, 15624], 'label': '31104.fx.108.es1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bi1', 'old_label': '108.es1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.es1', 'subgroup_fusion': None, 'weyl_group': '576.8654'}
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id: 186248294
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.et1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.by1', '36.cf1', '54.cc1'], 'contains': ['216.hp1', '324.dr1', '324.dv1', '1728.bz1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [6, 2592, 15984, 10444, 15552, 28464, 15624], 'label': '31104.fx.108.et1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bh1', 'old_label': '108.et1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.et1', 'subgroup_fusion': None, 'weyl_group': '576.8654'}
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id: 186248295
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.eu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ep1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.cc1', '36.ce1', '36.cj1', '54.ba1', '54.bm1', '54.ce1'], 'contains': ['216.da1', '216.ds1', '216.gw1', '324.ds1', '324.dt1'], 'core': '648.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [6, 12096, 18576, 18144, 22752, 15552, 16056], 'label': '31104.fx.108.eu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '108.eu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.eu1', 'subgroup_fusion': None, 'weyl_group': '864.4000'}
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id: 186248296
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.ev1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.cf1', '36.cg1', '36.ck1', '54.s1', '54.bn1', '54.cd1'], 'contains': ['216.gy1', '324.ds1', '324.du1', '324.dv1', '432.nc1'], 'core': '648.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [26047, 2592, 18576, 3100, 15552, 10368, 16056], 'label': '31104.fx.108.ev1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '108.ev1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ev1', 'subgroup_fusion': None, 'weyl_group': '3456.di'}
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id: 186248297
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.ew1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.ch1', '36.ci1', '36.cl1', '54.bo1'], 'contains': ['216.hb2', '324.ds1', '324.dw1', '432.nd1'], 'core': '648.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [6, 18144, 432, 19536, 15552, 22752, 16056], 'label': '31104.fx.108.ew1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1', 'old_label': '108.ew1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ew1', 'subgroup_fusion': None, 'weyl_group': '1728.46101'}
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id: 186248298
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.ex1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cm1', '36.cn1', '36.co1', '36.cp1', '36.cq1', '54.bd1', '54.bk1'], 'contains': ['216.b1', '216.db1', '216.dv1', '216.fe1', '216.gj1', '324.dx1', '324.dy1'], 'core': '216.b1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [10405, 2592, 10368, 16056, 15552, 18576, 22752], 'label': '31104.fx.108.ex1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '108.ex1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ex1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
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id: 186248299
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.ey1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.cm1', '36.cr1', '54.be1', '54.bg1', '54.bm1'], 'contains': ['216.dc1', '216.dp1', '216.ff1', '216.ge1', '216.gw1', '324.dx1', '324.dz1'], 'core': '648.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [10405, 15552, 2592, 16056, 1728, 18576, 22752], 'label': '31104.fx.108.ey1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '108.ey1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ey1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186248300
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.ez1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.cn1', '36.cs1', '54.u1'], 'contains': ['216.fg1', '216.gg1', '216.gx1', '324.dx1', '324.ea1', '432.fh1'], 'core': '648.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [10405, 18216, 12940, 18576, 18144, 10368, 15552], 'label': '31104.fx.108.ez1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '108.ez1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ez1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
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id: 186248301
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.fa1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.co1', '36.cs1', '54.v1', '54.bj1', '54.bn1'], 'contains': ['216.gy1', '324.dx1', '324.eb1', '432.fj1', '432.ni1'], 'core': '648.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [10405, 2592, 432, 22752, 15552, 16080, 16056], 'label': '31104.fx.108.fa1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '108.fa1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fa1', 'subgroup_fusion': None, 'weyl_group': '384.17948'}
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id: 186248302
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '18.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['9.d1'], 'contains': ['36.g1', '36.i1', '36.j1', '36.m1', '36.n1', '36.q1', '36.r1', '54.a1', '54.b1', '54.c1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [21265, 10368, 15984, 18576, 15558, 18648, 22752, 12096, 36], 'label': '31104.fx.18.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '18.a1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.a1', 'subgroup_fusion': None, 'weyl_group': '1728.39001'}
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id: 186248303
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.fb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.co1', '36.cr1', '36.cs1', '36.ct1', '54.w1', '54.bh1', '54.bu1'], 'contains': ['216.a1', '324.dx1', '324.eb1', '432.fk1', '432.nj1'], 'core': '216.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [10405, 2592, 432, 10368, 15552, 16080, 16056], 'label': '31104.fx.108.fb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '108.fb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fb1', 'subgroup_fusion': None, 'weyl_group': '384.17948'}
-
id: 186248304
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.fc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.cp1', '36.ct1'], 'contains': ['216.fh1', '216.gi1', '216.ha1', '324.dx1', '324.ec1', '432.fl1'], 'core': '648.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [10405, 3096, 29404, 18576, 15552, 10368, 2592], 'label': '31104.fx.108.fc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cp1', 'old_label': '108.fc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fc1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186248305
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.fd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.cq1', '36.cr1', '54.bi1'], 'contains': ['216.hb1', '324.dx1', '324.ed1', '432.fn1', '432.nk1'], 'core': '648.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [10405, 2592, 432, 10368, 15552, 9168, 16056], 'label': '31104.fx.108.fd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.y1', 'old_label': '108.fd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fd1', 'subgroup_fusion': None, 'weyl_group': '192.955'}
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id: 186248306
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.fd2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.cq1', '36.ct1', '54.bo1'], 'contains': ['216.hb2', '324.dx1', '324.ed1', '432.fn2', '432.nk2'], 'core': '648.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [10405, 2592, 432, 22752, 15552, 9168, 16056], 'label': '31104.fx.108.fd2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.y1', 'old_label': '108.fd2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fd2', 'subgroup_fusion': None, 'weyl_group': '192.955'}
-
id: 186248307
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.fe1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cm1', '36.cu1', '54.bf1'], 'contains': ['216.dd1', '216.dy1', '216.fi1', '216.fj1', '216.gl1', '216.gm1', '216.hc1', '324.dy1', '324.dz1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [10405, 15552, 2592, 16056, 1728, 18576, 12384], 'label': '31104.fx.108.fe1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '108.fe1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fe1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 186248308
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.ff1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cn1', '36.cw1', '54.x1'], 'contains': ['216.fk1', '216.gp1', '216.hd1', '324.dy1', '324.ea1', '432.fq1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [10405, 18216, 12940, 18576, 18144, 2016, 15552], 'label': '31104.fx.108.ff1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '108.ff1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ff1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
-
id: 186248309
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.fg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cn1', '36.cu1', '36.cv1', '36.cw1', '54.y1'], 'contains': ['216.fl1', '216.gr1', '216.he1', '324.dy1', '324.ea1', '432.fr1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [10405, 18216, 12940, 18576, 18144, 12384, 15552], 'label': '31104.fx.108.fg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '108.fg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fg1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
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id: 186248310
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.fh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.co1', '36.cw1', '54.z1'], 'contains': ['216.hf1', '324.dy1', '324.eb1', '432.fu1', '432.fv1', '432.nm1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [10405, 2592, 432, 12384, 15552, 16080, 16056], 'label': '31104.fx.108.fh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '108.fh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fh1', 'subgroup_fusion': None, 'weyl_group': '192.1538'}
-
id: 186248311
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.fi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cp1', '36.cu1'], 'contains': ['216.fm1', '216.gu1', '216.hh1', '324.dy1', '324.ec1', '432.fw1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [10405, 3096, 29404, 18576, 15552, 2016, 2592], 'label': '31104.fx.108.fi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cp1', 'old_label': '108.fi1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fi1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
-
id: 186248312
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.fi2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cp1', '36.cv1'], 'contains': ['216.fn1', '216.gv1', '216.hh2', '324.dy1', '324.ec1', '432.fx1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [10405, 3096, 29404, 18576, 15552, 12384, 2592], 'label': '31104.fx.108.fi2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cp1', 'old_label': '108.fi2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fi2', 'subgroup_fusion': None, 'weyl_group': '48.48'}
-
id: 186248313
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '18.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.d1'], 'contains': ['36.c1', '36.d1', '36.e1', '36.f1', '36.g1', '36.h1', '36.k1', '36.o1', '36.s1', '36.dk1', '36.dl1', '36.dm1', '36.dn1', '54.d1', '54.e1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [5713, 10368, 2592, 18576, 6, 16056, 22752, 12096, 36], 'label': '31104.fx.18.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '18.b1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.b1', 'subgroup_fusion': None, 'weyl_group': '1728.39001'}
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id: 186248314
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.fj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.cq1', '36.cv1'], 'contains': ['216.hi1', '324.dy1', '324.ed1', '432.ga1', '432.gb1', '432.nn1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [10405, 2592, 18576, 12384, 15552, 24268, 16056], 'label': '31104.fx.108.fj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cq1', 'old_label': '108.fj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fj1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
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id: 186248315
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.fk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cs1', '36.cw1', '54.p1', '54.bl1'], 'contains': ['216.hl1', '324.ea1', '324.eb1', '432.gc1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [10405, 18144, 15984, 12460, 15552, 16080, 15624], 'label': '31104.fx.108.fk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '108.fk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fk1', 'subgroup_fusion': None, 'weyl_group': '576.8654'}
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id: 186248316
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.fl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.cx1', '36.cy1', '36.cz1', '54.be1', '54.bp1', '54.ce1'], 'contains': ['216.dj1', '216.dt1', '216.fw1', '216.gf1', '216.gw1', '324.ee1', '324.ef1'], 'core': '648.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1, 15552, 2592, 16056, 22752, 18576, 1728], 'label': '31104.fx.108.fl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '108.fl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fl1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186248317
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.fm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cz1', '36.da1', '36.db1', '54.bf1'], 'contains': ['216.dk1', '216.dz1', '216.fx1', '216.fy1', '216.gn1', '216.go1', '216.hc1', '324.ee1', '324.eg1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1, 15552, 2592, 16056, 12384, 18576, 1728], 'label': '31104.fx.108.fm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '108.fm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fm1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186248318
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.fn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.dc1', '36.dd1', '36.de1', '54.u1'], 'contains': ['216.fz1', '216.gh1', '216.gx1', '324.ef1', '324.eh1', '324.ej1', '432.gn1'], 'core': '648.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1, 18216, 22752, 18576, 18144, 15552, 10924], 'label': '31104.fx.108.fn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.u1', 'old_label': '108.fn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fn1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
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id: 186248319
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.fo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.dc1', '36.dd1', '36.df1', '54.v1', '54.bq1', '54.cd1'], 'contains': ['216.gy1', '324.ef1', '324.ei1', '324.ek1', '432.gp1', '432.nw1'], 'core': '648.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1, 2592, 18576, 76, 15552, 10368, 16056], 'label': '31104.fx.108.fo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '108.fo1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fo1', 'subgroup_fusion': None, 'weyl_group': '1152.155790'}
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id: 186248320
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.fp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.cx1', '36.dd1', '36.df1', '54.w1', '54.bv1', '54.bw1'], 'contains': ['216.a1', '324.ef1', '324.ei1', '432.gq1', '432.nx1'], 'core': '216.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1, 2592, 432, 5712, 15552, 10368, 16056], 'label': '31104.fx.108.fp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '108.fp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fp1', 'subgroup_fusion': None, 'weyl_group': '3456.gu'}
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id: 186248321
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.fq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.cy1', '36.dc1', '36.df1', '54.bx1'], 'contains': ['216.gz1', '324.ef1', '324.ek1', '432.gr1', '432.ny1'], 'core': '648.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1, 2592, 432, 28464, 15552, 10368, 16056], 'label': '31104.fx.108.fq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bl1', 'old_label': '108.fq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fq1', 'subgroup_fusion': None, 'weyl_group': '1728.12469'}
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id: 186248322
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.fr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cz1', '36.de1', '36.df1', '54.bd1', '54.br1', '54.by1'], 'contains': ['216.b1', '216.dl1', '216.dx1', '216.ga1', '216.gk1', '324.ef1', '324.eg1'], 'core': '216.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1, 22752, 15552, 16056, 10368, 18576, 2592], 'label': '31104.fx.108.fr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '108.fr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fr1', 'subgroup_fusion': None, 'weyl_group': '288.977'}
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id: 186248323
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.fs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.de1', '36.dg1', '36.dh1', '54.x1'], 'contains': ['216.gb1', '216.gq1', '216.hd1', '324.eg1', '324.eh1', '324.ej1', '432.gt1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1, 18216, 2016, 18576, 18144, 15552, 10924], 'label': '31104.fx.108.fs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '108.fs1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fs1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
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id: 186248324
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '18.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.d1'], 'contains': ['36.h1', '36.i1', '36.u1', '36.w1', '36.x1', '54.f1', '54.g1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [5713, 10368, 15984, 18576, 15558, 18648, 22752, 12096, 36], 'label': '31104.fx.18.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '18.c1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.c1', 'subgroup_fusion': None, 'weyl_group': '1728.39001'}
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id: 186248325
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.ft1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.da1', '36.de1', '36.dh1', '54.y1'], 'contains': ['216.gc1', '216.gs1', '216.he1', '324.eg1', '324.eh1', '432.gu1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1, 18216, 12384, 18576, 18144, 15552, 556], 'label': '31104.fx.108.ft1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.r1', 'old_label': '108.ft1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ft1', 'subgroup_fusion': None, 'weyl_group': '864.4000'}
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id: 186248326
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.fu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.df1', '36.dg1', '36.dh1', '54.z1'], 'contains': ['216.hf1', '324.eg1', '324.ei1', '324.ek1', '432.gx1', '432.gy1', '432.oa1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1, 2592, 18576, 76, 15552, 12384, 16056], 'label': '31104.fx.108.fu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.z1', 'old_label': '108.fu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fu1', 'subgroup_fusion': None, 'weyl_group': '576.8660'}
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id: 186248327
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.fv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.db1', '36.de1', '36.dg1'], 'contains': ['216.gd1', '216.gt1', '216.hg1', '324.eg1', '324.ej1', '432.gz1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1, 18216, 12384, 18576, 18144, 15552, 10924], 'label': '31104.fx.108.fv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.db1', 'old_label': '108.fv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fv1', 'subgroup_fusion': None, 'weyl_group': '432.535'}
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id: 186248328
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.fw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.dc1', '36.dd1', '36.dg1', '36.dh1'], 'contains': ['216.hj1', '324.eh1', '324.ei1', '324.ej1', '324.ek1', '432.hb1', '432.hd1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1, 18144, 15984, 22828, 15552, 5712, 15624], 'label': '31104.fx.108.fw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.fw1', 'old_label': '108.fw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fw1', 'subgroup_fusion': None, 'weyl_group': '288.1026'}
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id: 186248329
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.fx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dc1', '36.dg1', '36.dh1'], 'contains': ['216.hk1', '324.eh1', '324.ej1', '324.ek1', '432.hc1', '432.he1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1, 18144, 15984, 2092, 15552, 28464, 15624], 'label': '31104.fx.108.fx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.fx1', 'old_label': '108.fx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fx1', 'subgroup_fusion': None, 'weyl_group': '288.1026'}
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id: 186248330
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.fy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dd1', '36.dh1', '54.p1', '54.bs1', '54.bz1'], 'contains': ['216.hl1', '324.eh1', '324.ei1', '432.hf1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [1, 18144, 15984, 20812, 15552, 5712, 15624], 'label': '31104.fx.108.fy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.fy1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fy1', 'subgroup_fusion': None, 'weyl_group': '576.8654'}
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id: 186248331
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.fz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dc1', '36.dh1', '54.ca1'], 'contains': ['216.hm1', '324.eh1', '324.ek1', '432.hg1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1, 18144, 15984, 76, 15552, 28464, 15624], 'label': '31104.fx.108.fz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.ca1', 'old_label': '108.fz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fz1', 'subgroup_fusion': None, 'weyl_group': '576.8654'}
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id: 186248332
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.ga1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.dc1', '36.dd1', '36.dg1', '54.cb1'], 'contains': ['216.hn1', '324.ei1', '324.ej1', '324.ek1', '432.hh1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1, 18144, 15984, 76, 15552, 5712, 15624], 'label': '31104.fx.108.ga1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.cb1', 'old_label': '108.ga1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ga1', 'subgroup_fusion': None, 'weyl_group': '576.8654'}
-
id: 186248333
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.gb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dd1', '36.dg1', '54.bt1'], 'contains': ['216.ho1', '324.ei1', '324.ej1', '432.hi1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1, 18144, 15984, 12460, 15552, 5712, 15624], 'label': '31104.fx.108.gb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bt1', 'old_label': '108.gb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.gb1', 'subgroup_fusion': None, 'weyl_group': '576.8654'}
-
id: 186248334
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.gc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dc1', '36.dg1'], 'contains': ['216.hp2', '324.ej1', '324.ek1', '432.hj1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1, 18144, 15984, 22828, 15552, 28464, 15624], 'label': '31104.fx.108.gc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.gc1', 'old_label': '108.gc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.gc1', 'subgroup_fusion': None, 'weyl_group': '288.1026'}
-
id: 186248335
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['9.d1'], 'contains': ['36.k1', '36.l1', '36.n1', '36.p1', '36.r1', '36.t1', '36.u1', '54.h1', '54.i1', '54.j1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [21265, 10368, 15984, 18576, 6, 18648, 22752, 12096, 15588], 'label': '31104.fx.18.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '18.d1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.d1', 'subgroup_fusion': None, 'weyl_group': '1728.39001'}
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id: 186248336
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.gc2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dc1', '36.dg1', '54.cc1'], 'contains': ['216.hp1', '324.ej1', '324.ek1', '432.hj2'], 'core': '1944.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1, 18144, 15984, 10444, 15552, 28464, 15624], 'label': '31104.fx.108.gc2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.cc1', 'old_label': '108.gc2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.gc2', 'subgroup_fusion': None, 'weyl_group': '576.8654'}
-
id: 186248337
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.gd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['27.b1', '36.dj1'], 'contains': ['216.jr1', '216.js1', '216.ju1', '216.ku1', '216.lh1', '216.ln1', '216.mc1', '324.el1', '324.er1', '432.oj1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [20737, 18576, 22752, 24198, 2592, 36, 16080], 'label': '31104.fx.108.gd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.gd1', 'old_label': '108.gd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.gd1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
-
id: 186248338
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.ge1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['27.c1', '36.di1', '36.dj1'], 'contains': ['216.jq1', '216.jt1', '216.jv1', '216.kr1', '216.lm1', '216.lp1', '216.lz1', '324.el1', '324.eq1', '432.ok1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1, 18576, 10368, 24198, 2592, 36, 16080], 'label': '31104.fx.108.ge1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ge1', 'old_label': '108.ge1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ge1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186248339
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.gf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.dk1', '54.d1'], 'contains': ['216.hq1', '216.hr1', '216.ib1', '216.ic1', '216.ii1', '216.ij1', '216.jm1', '216.jn1', '216.jx1', '216.kf1', '216.kj1', '216.ko1', '216.kp1', '216.lx1', '216.ly1', '324.em1', '324.en1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 12096, 18576, 2598, 10368, 36, 16056], 'label': '31104.fx.108.gf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '108.gf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.gf1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
-
id: 186248340
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.gg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.dk1', '54.e1'], 'contains': ['216.hs1', '216.hv1', '216.ia1', '216.id1', '216.is1', '216.iv1', '216.jg1', '216.jj1', '216.kb1', '216.ke1', '216.kl1', '216.la1', '216.ld1', '216.lq1', '216.lt1', '324.em1', '324.eo1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 22752, 18576, 24270, 10368, 36, 2592], 'label': '31104.fx.108.gg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '108.gg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.gg1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
-
id: 186248341
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.gh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.dk1', '54.d1'], 'contains': ['216.ht1', '216.hu1', '216.ib1', '216.ic1', '216.it1', '216.iu1', '216.jh1', '216.ji1', '216.jz1', '216.kg1', '216.ki1', '216.lb1', '216.lc1', '216.lr1', '216.ls1', '324.en1', '324.eo1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 12096, 18576, 2598, 22752, 36, 16056], 'label': '31104.fx.108.gh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '108.gh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.gh1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186248342
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.gi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.di1', '36.dl1', '54.d1'], 'contains': ['216.hq1', '216.hr1', '216.hw1', '216.hx1', '216.ig1', '216.ih1', '216.iy1', '216.iz1', '216.jy1', '216.jz1', '216.kg1', '216.kq1', '216.kz1', '216.le1', '216.mf1', '324.ep1', '324.eq1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 12096, 18576, 6, 22752, 36, 16056], 'label': '31104.fx.108.gi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '108.gi1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.gi1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186248343
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.gj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.dl1', '54.d1'], 'contains': ['216.ht1', '216.hu1', '216.hw1', '216.hx1', '216.iq1', '216.ir1', '216.iw1', '216.ix1', '216.jx1', '216.kc1', '216.kf1', '216.km1', '216.lg1', '216.ll1', '216.md1', '324.ep1', '324.er1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 12096, 18576, 6, 10368, 36, 16056], 'label': '31104.fx.108.gj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '108.gj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.gj1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
-
id: 186248344
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.gk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.dj1', '36.dl1', '54.e1'], 'contains': ['216.hs1', '216.hv1', '216.hy1', '216.hz1', '216.im1', '216.in1', '216.jc1', '216.jd1', '216.kb1', '216.kd1', '216.ke1', '216.ky1', '216.lf1', '216.lo1', '216.mb1', '324.eq1', '324.er1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 22752, 18576, 24198, 10368, 36, 2592], 'label': '31104.fx.108.gk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '108.gk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.gk1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
-
id: 186248345
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.gl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.dm1', '54.d1'], 'contains': ['216.ie1', '216.if1', '216.ig1', '216.ih1', '216.jh1', '216.ji1', '216.jo1', '216.jp1', '216.km1', '216.kn1', '216.kp1', '216.lu1', '216.lx1', '216.md1', '216.mh1', '324.es1', '324.et1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 12096, 18576, 6, 10368, 2628, 16056], 'label': '31104.fx.108.gl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '108.gl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.gl1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
-
id: 186248346
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '18.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.d1'], 'contains': ['36.l1', '36.m1', '36.o1', '36.v1', '36.x1', '54.k1', '54.l1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [5713, 10368, 15984, 18576, 15558, 18648, 22752, 12096, 15588], 'label': '31104.fx.18.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '18.e1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.e1', 'subgroup_fusion': None, 'weyl_group': '1728.39001'}
-
id: 186248347
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.gm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.dm1', '54.e1'], 'contains': ['216.ik1', '216.il1', '216.im1', '216.in1', '216.jg1', '216.jj1', '216.jk1', '216.jl1', '216.kx1', '216.ky1', '216.ld1', '216.lq1', '216.lw1', '216.mb1', '216.mg1', '324.es1', '324.ev1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 22752, 18576, 24198, 10368, 108, 2592], 'label': '31104.fx.108.gm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '108.gm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.gm1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
-
id: 186248348
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.gn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.dm1', '54.d1'], 'contains': ['216.io1', '216.ip1', '216.iq1', '216.ir1', '216.jm1', '216.jn1', '216.jo1', '216.jp1', '216.kv1', '216.kz1', '216.lc1', '216.lr1', '216.me1', '216.mf1', '216.mi1', '324.et1', '324.ev1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 12096, 18576, 6, 22752, 2628, 16056], 'label': '31104.fx.108.gn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '108.gn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.gn1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
-
id: 186248349
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.go1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.dn1', '54.d1'], 'contains': ['216.ie1', '216.if1', '216.ii1', '216.ij1', '216.iw1', '216.ix1', '216.ja1', '216.jb1', '216.kq1', '216.kt1', '216.kv1', '216.lb1', '216.le1', '216.ls1', '216.mi1', '324.eu1', '324.ew1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 12096, 18576, 2598, 22752, 2628, 16056], 'label': '31104.fx.108.go1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '108.go1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.go1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
-
id: 186248350
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.gp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.dn1', '54.d1'], 'contains': ['216.io1', '216.ip1', '216.it1', '216.iu1', '216.iy1', '216.iz1', '216.ja1', '216.jb1', '216.kn1', '216.ko1', '216.lg1', '216.lj2', '216.ll1', '216.ly1', '216.mh1', '324.eu1', '324.ex1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 12096, 18576, 2598, 10368, 2628, 16056], 'label': '31104.fx.108.gp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '108.gp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.gp1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
-
id: 186248351
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '108.gq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.dn1', '54.e1'], 'contains': ['216.ik1', '216.il1', '216.is1', '216.iv1', '216.jc1', '216.jd1', '216.je1', '216.jf1', '216.kx1', '216.la1', '216.lf1', '216.lk1', '216.lo1', '216.lt1', '216.mg1', '324.ew1', '324.ex1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 22752, 18576, 24270, 10368, 108, 2592], 'label': '31104.fx.108.gq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '108.gq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.gq1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
-
id: 186248352
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '128.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1', '64.a1', '64.b1', '64.c1', '64.d1', '64.e1'], 'contains': ['384.a1', '384.b1', '384.c1', '384.d1', '384.e1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [18580, 5712, 12096], 'label': '31104.fx.128.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.d1', 'old_label': '128.a1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.a1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
-
id: 186248353
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.c1', '72.w1', '72.bw1'], 'contains': ['288.a1', '288.e1', '288.o1', '288.cb1', '288.cf1', '432.a1', '432.b1', '432.c1', '432.d1', '432.e1', '432.f1', '432.g1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [36, 10368, 22752, 16056, 15552, 12096], 'label': '31104.fx.144.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '144.a1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.a1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
-
id: 186248354
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.c1', '72.d1', '72.bx1'], 'contains': ['288.a1', '288.f1', '288.t1', '432.h1', '432.i1', '432.j1', '432.k1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [10405, 1728, 15552, 16056, 22752, 10368], 'label': '31104.fx.144.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bc1', 'old_label': '144.b1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 186248355
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.w1', '72.ba1', '72.ce1'], 'contains': ['288.a1', '288.m1', '288.o1', '288.cf1', '288.ch1', '432.l1', '432.l2', '432.m1', '432.n1', '432.o1', '432.p1', '432.q1', '432.r1', '432.r2'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [18612, 10368, 22752, 16056, 15552, 12096], 'label': '31104.fx.144.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1', 'old_label': '144.c1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.c1', 'subgroup_fusion': None, 'weyl_group': '54.14'}
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id: 186248356
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1', '72.ba1', '72.bw1'], 'contains': ['288.a1', '288.m1', '288.n1', '288.cf1', '288.cg1', '432.s1', '432.t1', '432.u1', '432.v1', '432.w1', '432.x1', '432.y1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [2628, 10368, 22752, 16056, 15552, 12096], 'label': '31104.fx.144.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '144.d1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.d1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
-
id: 186248357
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '18.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.d1'], 'contains': ['36.p1', '36.q1', '36.s1', '36.v1', '36.w1', '54.m1', '54.n1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [5713, 10368, 15984, 18576, 6, 18648, 22752, 12096, 15588], 'label': '31104.fx.18.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '18.f1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.f1', 'subgroup_fusion': None, 'weyl_group': '1728.39001'}
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id: 186248358
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.c1', '72.d1', '72.cf1'], 'contains': ['288.a1', '288.p1', '288.u1', '432.z1', '432.ba1', '432.bb1', '432.bc1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1, 10368, 22752, 16056, 12096, 15552], 'label': '31104.fx.144.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bc1', 'old_label': '144.e1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.e1', 'subgroup_fusion': None, 'weyl_group': '72.49'}
-
id: 186248359
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.y1', '48.a1', '72.bj1'], 'contains': ['288.b1', '288.g1', '288.s1', '288.dc1', '288.ec1', '432.bd1', '432.be1', '432.bf1', '432.bj1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [1, 10368, 2016, 36, 15552, 10924], 'label': '31104.fx.144.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bj1', 'old_label': '144.f1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.f1', 'subgroup_fusion': None, 'weyl_group': '216.171'}
-
id: 186248360
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.z1', '48.a1', '72.bn1'], 'contains': ['288.c1', '288.i1', '288.q1', '288.df1', '288.ef1', '432.bf1', '432.bl1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [20737, 12384, 1728, 36, 15552, 556], 'label': '31104.fx.144.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bn1', 'old_label': '144.g1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.g1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
-
id: 186248361
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ba1', '48.b1', '72.bj1'], 'contains': ['288.b1', '288.v1', '288.w1', '432.bg1', '432.bh1', '432.bi1', '432.bo1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [505, 10368, 2016, 36, 15552, 29068], 'label': '31104.fx.144.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bj1', 'old_label': '144.h1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.h1', 'subgroup_fusion': None, 'weyl_group': '216.171'}
-
id: 186248362
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bb1', '48.b1', '72.bn1'], 'contains': ['288.c1', '288.y1', '288.z1', '432.bi1', '432.bp1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [21241, 12384, 1728, 36, 15552, 18700], 'label': '31104.fx.144.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bn1', 'old_label': '144.i1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.i1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
-
id: 186248363
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1', '72.c1', '72.f1', '72.bp1'], 'contains': ['288.e1', '288.f1', '288.p1', '288.dh1', '288.ed1', '432.bj1', '432.bk1', '432.bl1', '432.bm1'], 'core': '576.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1, 10368, 22752, 36, 18144, 12096], 'label': '31104.fx.144.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bc1', 'old_label': '144.j1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.j1', 'subgroup_fusion': None, 'weyl_group': '216.171'}
-
id: 186248364
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1', '72.c1', '72.h1', '72.bp1'], 'contains': ['288.e1', '288.t1', '288.u1', '432.bn1', '432.bo1', '432.bp1', '432.bq1'], 'core': '576.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [15625, 10368, 22752, 36, 18144, 12096], 'label': '31104.fx.144.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bc1', 'old_label': '144.k1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.k1', 'subgroup_fusion': None, 'weyl_group': '216.171'}
-
id: 186248365
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.be1', '48.c1', '72.bj1'], 'contains': ['288.g1', '288.j1', '288.w1', '432.bs1', '432.bu1', '432.bv1', '432.bw1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [505, 10368, 2016, 18684, 15552, 29068], 'label': '31104.fx.144.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bj1', 'old_label': '144.l1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.l1', 'subgroup_fusion': None, 'weyl_group': '216.171'}
-
id: 186248366
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1', '72.f1', '72.br1'], 'contains': ['288.f1', '288.m1', '288.p1', '288.ed1', '288.ee1', '432.br1', '432.bx1', '432.by1', '432.bz1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1, 10368, 22752, 2628, 18144, 12096], 'label': '31104.fx.144.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bc1', 'old_label': '144.m1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.m1', 'subgroup_fusion': None, 'weyl_group': '216.171'}
-
id: 186248367
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1', '72.d1', '72.p1', '72.bp1'], 'contains': ['288.f1', '288.n1', '288.u1', '432.bs1', '432.ca1', '432.cb1', '432.cc1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [15625, 10368, 22752, 18252, 18144, 12096], 'label': '31104.fx.144.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bc1', 'old_label': '144.n1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.n1', 'subgroup_fusion': None, 'weyl_group': '216.171'}
-
id: 186248368
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '18.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.c1', '9.a1'], 'contains': ['36.bk1', '36.br1', '36.cg1', '54.o1', '54.q1', '54.s1', '288.cu1'], 'core': '216.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [24198, 15552, 22752, 15624, 36, 16080, 2592, 15984, 20812], 'label': '31104.fx.18.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.g1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.g1', 'subgroup_fusion': None, 'weyl_group': '3456.di'}
-
id: 186248369
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.c1', '72.p1', '72.br1'], 'contains': ['288.f1', '288.o1', '288.u1', '432.bt1', '432.cd1', '432.ce1', '432.cf1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [15625, 10368, 22752, 15660, 18144, 12096], 'label': '31104.fx.144.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bc1', 'old_label': '144.o1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.o1', 'subgroup_fusion': None, 'weyl_group': '216.171'}
-
id: 186248370
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bg1', '48.c1', '72.bn1'], 'contains': ['288.i1', '288.k1', '288.z1', '432.bw1', '432.cb1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [21241, 12384, 1728, 18684, 15552, 18700], 'label': '31104.fx.144.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bn1', 'old_label': '144.p1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.p1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
-
id: 186248371
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bh1', '48.d1', '72.bn1'], 'contains': ['288.k1', '288.q1', '288.y1', '432.ci1', '432.co1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [20737, 12384, 1728, 18684, 15552, 556], 'label': '31104.fx.144.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bn1', 'old_label': '144.q1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.q1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
-
id: 186248372
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bi1', '48.d1', '72.bj1'], 'contains': ['288.j1', '288.s1', '288.v1', '432.cg1', '432.ch1', '432.ci1', '432.cq1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [1, 10368, 2016, 18684, 15552, 10924], 'label': '31104.fx.144.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bj1', 'old_label': '144.r1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.r1', 'subgroup_fusion': None, 'weyl_group': '216.171'}
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id: 186248373
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1', '72.h1', '72.br1'], 'contains': ['288.m1', '288.t1', '288.u1', '432.cj1', '432.ck1', '432.cl1', '432.cm1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [15625, 10368, 22752, 2628, 18144, 12096], 'label': '31104.fx.144.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bc1', 'old_label': '144.s1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.s1', 'subgroup_fusion': None, 'weyl_group': '216.171'}
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id: 186248374
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.d1', '72.d1', '72.r1', '72.bp1'], 'contains': ['288.n1', '288.p1', '288.t1', '432.cn1', '432.co1', '432.cp1', '432.cq1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1, 10368, 22752, 18252, 18144, 12096], 'label': '31104.fx.144.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bc1', 'old_label': '144.t1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.t1', 'subgroup_fusion': None, 'weyl_group': '216.171'}
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id: 186248375
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.c1', '72.r1', '72.br1'], 'contains': ['288.o1', '288.p1', '288.t1', '432.cr1', '432.cs1', '432.ct1', '432.cu1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1, 10368, 22752, 15660, 18144, 12096], 'label': '31104.fx.144.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bc1', 'old_label': '144.u1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.u1', 'subgroup_fusion': None, 'weyl_group': '216.171'}
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id: 186248376
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1', '72.f1', '72.g1', '72.h1', '72.w1', '72.bw1'], 'contains': ['288.e1', '288.m1', '288.bb1', '288.cb1', '288.cg1', '432.cv1', '432.cw1', '432.cx1', '432.cy1', '432.cz1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [36, 10368, 22752, 18144, 16056, 12096], 'label': '31104.fx.144.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '144.v1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.v1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
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id: 186248377
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.gc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.e1', '72.i1', '72.j1', '72.k1', '72.l1', '72.m1', '72.x1'], 'contains': ['288.bb1', '288.cc1', '288.cj1', '432.da1', '432.db1', '432.dc1', '432.dd1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [12138, 10368, 16056, 18144, 12096, 22752], 'label': '31104.fx.144.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '144.w1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.w1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186248378
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ep1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.e1', '72.i1', '72.j1', '72.k1', '72.n1', '72.o1', '72.y1'], 'contains': ['288.bb1', '288.cd1', '288.cl1', '432.de1', '432.df1', '432.dg1', '432.dh1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [6, 22752, 12096, 18144, 10368, 16056], 'label': '31104.fx.144.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '144.x1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.x1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186248379
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '18.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.c1', '9.a1'], 'contains': ['36.bk1', '36.bw1', '36.bz1', '54.o1', '54.r1', '54.t1', '288.cv1'], 'core': '108.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [24198, 15552, 10368, 15624, 36, 16080, 2592, 15984, 22828], 'label': '31104.fx.18.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.h1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.h1', 'subgroup_fusion': None, 'weyl_group': '3456.di'}
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id: 186248380
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.f1', '72.i1', '72.p1', '72.q1', '72.z1', '72.bx1'], 'contains': ['288.f1', '288.bb1', '288.ce1', '432.di1', '432.dj1', '432.dk1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [10405, 1728, 10368, 18144, 2592, 22752], 'label': '31104.fx.144.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '144.y1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.y1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186248381
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.p1', '72.r1', '72.s1', '72.t1', '72.ba1', '72.bw1', '72.ce1'], 'contains': ['288.m1', '288.n1', '288.o1', '288.bb1', '288.cf1', '432.dl1', '432.dm1', '432.dn1', '432.do1', '432.do2', '432.dp1', '432.dp2'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [15588, 10368, 22752, 18144, 16056, 12096], 'label': '31104.fx.144.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '144.z1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.z1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
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id: 186248382
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.j1', '72.q1', '72.u1', '72.v1', '72.w1', '72.ce1'], 'contains': ['288.o1', '288.bb1', '288.ch1', '432.dq1', '432.dr1', '432.ds1', '432.dt1', '432.du1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [468, 10368, 22752, 18144, 16056, 12096], 'label': '31104.fx.144.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '144.ba1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ba1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
-
id: 186248383
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.f1', '72.l1', '72.n1', '72.r1', '72.u1', '72.bb1', '72.cf1'], 'contains': ['288.p1', '288.bb1', '288.ci1', '432.dv1', '432.dw1', '432.dx1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1, 10368, 22752, 15552, 2592, 12096], 'label': '31104.fx.144.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '144.bb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bb1', 'subgroup_fusion': None, 'weyl_group': '288.977'}
-
id: 186248384
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.g1', '72.k1', '72.s1', '72.u1', '72.z1', '72.cj1'], 'contains': ['288.bb1', '288.ck1', '432.dy1', '432.ec1', '432.eg1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [10837, 1728, 2592, 15552, 22752, 10368], 'label': '31104.fx.144.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '144.bc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bc1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186248385
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.h1', '72.r1', '72.t1', '72.v1', '72.bd1', '72.bx1', '72.cj1'], 'contains': ['288.t1', '288.bb1', '432.dz1', '432.ed1', '432.eh1', '432.ei1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [26461, 1728, 15552, 2592, 22752, 10368], 'label': '31104.fx.144.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '144.bd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bd1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 186248386
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.g1', '72.m1', '72.o1', '72.q1', '72.t1', '72.bb1', '72.ck1'], 'contains': ['288.bb1', '288.cm1', '432.ea1', '432.ee1', '432.ej1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [433, 10368, 22752, 15552, 12096, 2592], 'label': '31104.fx.144.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '144.be1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.be1', 'subgroup_fusion': None, 'weyl_group': '288.977'}
-
id: 186248387
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.h1', '72.p1', '72.s1', '72.v1', '72.bf1', '72.cf1', '72.ck1'], 'contains': ['288.u1', '288.bb1', '432.eb1', '432.ef1', '432.ek1', '432.ek2'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [16057, 10368, 22752, 2592, 12096, 15552], 'label': '31104.fx.144.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '144.bf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bf1', 'subgroup_fusion': None, 'weyl_group': '144.196'}
-
id: 186248388
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1', '72.w1', '72.x1', '72.y1', '72.z1', '72.ba1', '72.bb1', '72.bc1', '72.bd1', '72.be1', '72.bf1'], 'contains': ['288.a1', '288.bb1', '288.cr1', '432.el1', '432.em1', '432.en1', '432.eo1', '432.ep1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [18576, 10368, 22752, 18144, 16056, 12096], 'label': '31104.fx.144.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '144.bg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bg1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 186248389
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.bk1', '48.e1', '72.bg1'], 'contains': ['288.bf1', '432.eq1', '432.er1', '432.es1', '432.et1', '432.eu1', '576.j1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [36, 10368, 15552, 22828, 16080, 18648], 'label': '31104.fx.144.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bg1', 'old_label': '144.bh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bh1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
-
id: 186248390
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['6.b1', '6.c1', '6.d1', '6.j1', '6.m1', '9.a1', '9.c1', '48.bc1'], 'core': '6.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 18576, 16080, 22752, 18144, 24198, 76, 16056, 10368, 15552, 36], 'label': '31104.fx.3.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '3.a1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1', 'subgroup_fusion': None, 'weyl_group': '10368.fj'}
-
id: 186248391
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '18.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.d1', '9.a1'], 'contains': ['36.bk1', '36.cs1', '36.dd1', '54.p1', '54.u1', '54.v1', '54.w1', '72.bg1'], 'core': '216.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1, 15552, 10368, 15624, 36, 16080, 18144, 15984, 22828], 'label': '31104.fx.18.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.i1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.i1', 'subgroup_fusion': None, 'weyl_group': '3456.di'}
-
id: 186248392
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bl1', '48.e1', '72.bh1'], 'contains': ['288.bw1', '432.eq1', '432.ew1', '432.ex1', '432.ez1', '576.k1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [36, 12384, 15552, 76, 16080, 18648], 'label': '31104.fx.144.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bh1', 'old_label': '144.bi1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bi1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186248393
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bl1', '48.e1', '72.bi1'], 'contains': ['288.by1', '432.eq1', '432.ev1', '432.ey1', '432.fa1', '576.k1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [36, 12384, 18144, 508, 16080, 72], 'label': '31104.fx.144.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bi1', 'old_label': '144.bj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bj1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186248394
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.bm1', '48.h1', '72.bm1'], 'contains': ['288.bc1', '432.eu1', '432.fb1', '576.l1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [36, 10368, 12096, 5712, 18648, 15552], 'label': '31104.fx.144.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bm1', 'old_label': '144.bk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bk1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
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id: 186248395
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ck1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bn1', '48.e1', '48.f1', '72.bj1'], 'contains': ['288.b1', '288.j1', '288.bj1', '432.er1', '432.ev1', '432.ew1', '432.fc1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [36, 10368, 2016, 3096, 15552, 10924], 'label': '31104.fx.144.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1', 'old_label': '144.bl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bl1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
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id: 186248396
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cl1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1', '48.g1', '72.bk1', '72.bt1'], 'contains': ['288.bk1', '432.es1', '432.ex1', '432.ey1', '432.fc1', '576.m1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [36, 10368, 2016, 10924, 72, 18144], 'label': '31104.fx.144.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '144.bm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bm1', 'subgroup_fusion': None, 'weyl_group': '432.746'}
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id: 186248397
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.bo1', '48.e1', '48.h1', '72.bl1'], 'contains': ['288.bl1', '432.et1', '432.eu1', '432.ez1', '432.fa1', '432.fc1', '576.n1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [36, 10368, 22752, 5712, 18648, 15552], 'label': '31104.fx.144.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1', 'old_label': '144.bn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bn1', 'subgroup_fusion': None, 'weyl_group': '432.746'}
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id: 186248398
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bp1', '48.f1', '72.bn1'], 'contains': ['288.c1', '288.d1', '288.k1', '288.l1', '288.bp1', '432.ew1', '432.fd1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [36, 12384, 12096, 15552, 18648, 556], 'label': '31104.fx.144.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bn1', 'old_label': '144.bo1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bo1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
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id: 186248399
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1', '72.bo1', '72.bu1', '72.bv1'], 'contains': ['288.bq1', '432.ey1', '432.fe1', '576.o1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [36, 12384, 12096, 556, 72, 18144], 'label': '31104.fx.144.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.r1', 'old_label': '144.bp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bp1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
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id: 186248400
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1', '48.g1', '48.h1', '72.bp1', '72.bw1'], 'contains': ['288.e1', '288.n1', '288.bi1', '432.fb1', '432.fc1', '432.fd1', '432.fe1'], 'core': '576.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [36, 10368, 22752, 3096, 15552, 12096], 'label': '31104.fx.144.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '144.bq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bq1', 'subgroup_fusion': None, 'weyl_group': '972.456'}
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id: 186248401
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1', '48.j1', '48.k1', '72.bp1', '72.br1', '72.bx1'], 'contains': ['288.f1', '288.t1', '288.bi1', '432.ff1', '432.fg1', '432.fo1', '432.fp1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [10405, 1728, 15552, 3096, 22752, 10368], 'label': '31104.fx.144.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bc1', 'old_label': '144.br1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.br1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186248402
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '18.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1'], 'contains': ['36.bl1', '36.cw1', '36.dh1', '54.p1', '54.x1', '54.y1', '54.z1', '72.bh1', '72.bi1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [20737, 15552, 12384, 15624, 36, 16080, 18144, 15984, 76], 'label': '31104.fx.18.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1', 'old_label': '18.j1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.j1', 'subgroup_fusion': None, 'weyl_group': '1728.47859'}
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id: 186248403
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cn1', '48.i1', '48.l1', '48.n1', '72.bj1'], 'contains': ['288.g1', '288.v1', '288.bj1', '432.ff1', '432.fh1', '432.fq1', '432.fr1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [10405, 12940, 15552, 3096, 22752, 10368], 'label': '31104.fx.144.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bj1', 'old_label': '144.bs1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bs1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 186248404
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.j1', '48.m1', '48.n1', '72.bk1', '72.bq1', '72.by1'], 'contains': ['288.bk1', '432.ff1', '432.fi1', '432.fs1', '432.ft1', '576.bn1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [10405, 18144, 72, 22752, 10368, 12940], 'label': '31104.fx.144.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.y1', 'old_label': '144.bt1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bt1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186248405
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.co1', '48.k1', '48.n1', '48.o1', '72.bl1'], 'contains': ['288.bl1', '432.ff1', '432.fj1', '432.fk1', '432.fu1', '432.fv1', '576.bo1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [10405, 15552, 18648, 22752, 10368, 12460], 'label': '31104.fx.144.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bl1', 'old_label': '144.bu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bu1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186248406
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cp1', '48.i1', '48.m1', '48.o1'], 'contains': ['288.h1', '288.x1', '288.bm1', '432.ff1', '432.fl1', '432.fw1', '432.fx1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [10405, 29404, 18144, 18216, 22752, 10368], 'label': '31104.fx.144.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.bv1', 'old_label': '144.bv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bv1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186248407
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.j1', '48.l1', '48.o1', '72.bz1'], 'contains': ['288.bn1', '432.ff1', '432.fm1', '432.fy1', '432.fz1', '576.bp1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [10405, 15552, 3096, 22752, 10368, 29404], 'label': '31104.fx.144.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bz1', 'old_label': '144.bw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bw1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186248408
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.cq1', '48.k1', '48.l1', '48.m1', '48.o1'], 'contains': ['288.bo1', '432.ff1', '432.fn1', '432.fn2', '432.ga1', '432.gb1', '576.bq1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [10405, 15552, 18648, 10368, 22752, 9168], 'label': '31104.fx.144.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.bx1', 'old_label': '144.bx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bx1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 186248409
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.cr1', '48.k1', '72.bm1'], 'contains': ['288.bc1', '432.fg1', '432.fk1', '432.fn1', '576.br1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [10405, 15552, 18648, 12460, 1728, 22752], 'label': '31104.fx.144.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '144.by1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.by1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186248410
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.cs1', '48.n1', '72.bg1'], 'contains': ['288.bf1', '432.fh1', '432.fi1', '432.fj1', '432.fk1', '432.gc1', '576.bs1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [10405, 15552, 18648, 10368, 12460, 16080], 'label': '31104.fx.144.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1', 'old_label': '144.bz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bz1', 'subgroup_fusion': None, 'weyl_group': '144.189'}
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id: 186248411
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.ct1', '48.o1'], 'contains': ['288.bg1', '432.fk1', '432.fl1', '432.fm1', '432.fn2', '576.bt1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [10405, 15552, 18648, 12460, 9168, 22752], 'label': '31104.fx.144.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.o1', 'old_label': '144.ca1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ca1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
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id: 186248412
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cu1', '48.i1', '72.bn1'], 'contains': ['288.i1', '288.y1', '288.bp1', '432.fo1', '432.fr1', '432.fw1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [10405, 12384, 1728, 3096, 15552, 12940], 'label': '31104.fx.144.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.d1', 'old_label': '144.cb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cb1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186248413
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '18.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.e1', '9.b1'], 'contains': ['36.bm1', '36.bq1', '36.cc1', '54.q1', '54.ba1', '72.ea1'], 'core': '216.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [6, 22752, 18576, 2592, 36, 2664, 12096, 15552, 20812], 'label': '31104.fx.18.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.k1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.k1', 'subgroup_fusion': None, 'weyl_group': '3456.gu'}
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id: 186248414
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.j1', '72.bo1', '72.bs1', '72.ca1'], 'contains': ['288.bq1', '432.fp1', '432.ft1', '432.fz1', '576.bu1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [10405, 18144, 72, 12940, 1728, 12384], 'label': '31104.fx.144.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1', 'old_label': '144.cc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cc1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186248415
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cv1', '48.l1'], 'contains': ['288.bu1', '432.fr1', '432.fy1', '432.ga1', '576.bv1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [10405, 15552, 18648, 24268, 9168, 12384], 'label': '31104.fx.144.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.l1', 'old_label': '144.cd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cd1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
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id: 186248416
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cw1', '48.n1', '72.bh1'], 'contains': ['288.bw1', '432.fr1', '432.fs1', '432.fu1', '432.gc1', '576.bw1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [10405, 15552, 18648, 12384, 12460, 16080], 'label': '31104.fx.144.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1', 'old_label': '144.ce1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ce1', 'subgroup_fusion': None, 'weyl_group': '144.189'}
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id: 186248417
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cv1', '48.m1'], 'contains': ['288.bx1', '432.ft1', '432.fx1', '432.gb1', '576.bv1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [10405, 18144, 18216, 24700, 9168, 12384], 'label': '31104.fx.144.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.m1', 'old_label': '144.cf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cf1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
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id: 186248418
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cw1', '48.n1', '72.bi1'], 'contains': ['288.by1', '432.fq1', '432.ft1', '432.fv1', '432.gc1', '576.bw1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [10405, 18144, 18216, 12384, 12892, 16080], 'label': '31104.fx.144.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1', 'old_label': '144.cg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cg1', 'subgroup_fusion': None, 'weyl_group': '144.189'}
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id: 186248419
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.p1', '72.bq1', '72.bt1', '72.cb1'], 'contains': ['288.bk1', '432.gd1', '432.ge1', '432.gf1', '432.gh1', '576.bx1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [468, 10368, 2016, 10924, 72, 18144], 'label': '31104.fx.144.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '144.ch1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ch1', 'subgroup_fusion': None, 'weyl_group': '432.746'}
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id: 186248420
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.p1', '72.bs1', '72.bu1', '72.cd1'], 'contains': ['288.bq1', '432.gf1', '432.gj1', '576.by1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [18612, 12384, 12096, 556, 18216, 18144], 'label': '31104.fx.144.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.r1', 'old_label': '144.ci1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ci1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
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id: 186248421
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.ci2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.p1', '72.bv1', '72.cc1', '72.cd1'], 'contains': ['288.bq1', '432.gf1', '432.gj2', '576.by2'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [3060, 12384, 12096, 556, 18216, 18144], 'label': '31104.fx.144.ci2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bp1', 'old_label': '144.ci2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ci2', 'subgroup_fusion': None, 'weyl_group': '216.99'}
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id: 186248422
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.p1', '72.br1', '72.bw1', '72.ce1'], 'contains': ['288.m1', '288.o1', '288.bi1', '432.gg1', '432.gh1', '432.gi1', '432.gj1', '432.gj2'], 'core': '1152.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [3060, 10368, 22752, 3096, 15552, 12096], 'label': '31104.fx.144.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '144.cj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cj1', 'subgroup_fusion': None, 'weyl_group': '324.124'}
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id: 186248423
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.cx1', '48.s1', '72.bm1'], 'contains': ['288.bc1', '432.gk1', '432.gq1', '576.cb1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [1, 15552, 18648, 1728, 20812, 22752], 'label': '31104.fx.144.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bm1', 'old_label': '144.ck1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ck1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
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id: 186248424
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '18.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.c1', '6.e1', '9.c1'], 'contains': ['36.bo1', '36.bt1', '36.ca1', '54.q1', '54.r1', '54.bc1', '72.eb1'], 'core': '72.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [19135, 10368, 15984, 2592, 36, 15624, 22752, 15552, 5712], 'label': '31104.fx.18.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '18.l1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.l1', 'subgroup_fusion': None, 'weyl_group': '3456.de'}
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id: 186248425
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.cy1', '48.s1'], 'contains': ['288.bd1', '432.gk1', '432.gr1', '576.cc1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [1, 15552, 18648, 1728, 76, 22752], 'label': '31104.fx.144.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.cl1', 'old_label': '144.cl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cl1', 'subgroup_fusion': None, 'weyl_group': '216.92'}
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id: 186248426
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.q1', '48.r1', '48.s1', '72.bp1', '72.br1', '72.cf1'], 'contains': ['288.p1', '288.u1', '288.bi1', '432.gk1', '432.gl1', '432.gm1', '432.gs1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1, 10368, 22752, 3096, 12096, 15552], 'label': '31104.fx.144.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bc1', 'old_label': '144.cm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cm1', 'subgroup_fusion': None, 'weyl_group': '72.49'}
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id: 186248427
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.da1', '48.q1', '72.bn1'], 'contains': ['288.q1', '288.z1', '288.bp1', '432.gl1', '432.gu1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [1, 12384, 556, 3096, 1728, 15552], 'label': '31104.fx.144.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bn1', 'old_label': '144.cn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cn1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
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id: 186248428
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.r1', '72.bo1', '72.bs1', '72.cg1'], 'contains': ['288.bq1', '432.gm1', '432.gw1', '576.ce1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1, 18144, 72, 1728, 556, 12384], 'label': '31104.fx.144.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.z1', 'old_label': '144.co1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.co1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
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id: 186248429
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.db1', '48.q1'], 'contains': ['288.r1', '288.ba1', '288.br1', '432.gl1', '432.gz1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [1, 12384, 10924, 3096, 1728, 15552], 'label': '31104.fx.144.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.cp1', 'old_label': '144.cp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cp1', 'subgroup_fusion': None, 'weyl_group': '108.25'}
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id: 186248430
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.r1', '72.ch1'], 'contains': ['288.bs1', '432.gm1', '432.ha1', '576.cf1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [1, 18144, 72, 1728, 10924, 12384], 'label': '31104.fx.144.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.ch1', 'old_label': '144.cq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cq1', 'subgroup_fusion': None, 'weyl_group': '216.92'}
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id: 186248431
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.dc1', '48.t1'], 'contains': ['288.be1', '432.gn1', '432.go1', '432.gp1', '432.gr1', '432.hb1', '432.hc1', '432.hd1', '432.he1', '432.hg1', '432.hh1', '432.hj1', '432.hj2', '576.cg1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [1, 15552, 18648, 76, 28464, 10368], 'label': '31104.fx.144.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.cr1', 'old_label': '144.cr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cr1', 'subgroup_fusion': None, 'weyl_group': '216.165'}
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id: 186248545
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '162.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.o1', '54.q1', '54.r1', '81.a1'], 'contains': ['324.df1', '324.dl1', '324.dq1', '486.g1', '648.id1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [24198, 2592, 18576, 36, 15552, 12460, 2664], 'label': '31104.fx.162.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '162.o1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.o1', 'subgroup_fusion': None, 'weyl_group': '192.955'}
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id: 186248432
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.dd1', '48.t1', '72.bg1'], 'contains': ['288.bf1', '432.gn1', '432.go1', '432.gp1', '432.gq1', '432.hb1', '432.hd1', '432.hf1', '432.hh1', '432.hi1', '576.ch1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [1, 15552, 18648, 76, 5712, 10368], 'label': '31104.fx.144.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bg1', 'old_label': '144.cs1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cs1', 'subgroup_fusion': None, 'weyl_group': '432.747'}
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id: 186248433
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.de1', '48.q1', '48.t1', '72.bj1'], 'contains': ['288.s1', '288.w1', '288.bj1', '432.gn1', '432.gs1', '432.gt1', '432.gu1', '432.gz1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [1, 12384, 10368, 3096, 15552, 10924], 'label': '31104.fx.144.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.d1', 'old_label': '144.ct1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ct1', 'subgroup_fusion': None, 'weyl_group': '648.610'}
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id: 186248434
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.r1', '48.t1', '72.bk1', '72.bq1', '72.ci1'], 'contains': ['288.bk1', '432.go1', '432.gs1', '432.gv1', '432.gw1', '432.ha1', '576.ci1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [1, 18144, 72, 10924, 22752, 12384], 'label': '31104.fx.144.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1', 'old_label': '144.cu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cu1', 'subgroup_fusion': None, 'weyl_group': '1296.2940'}
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id: 186248435
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '18.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.a1', '9.b1'], 'contains': ['36.bm1', '36.bv1', '36.cb1', '54.t1', '54.bb1', '72.ec1', '72.ed1'], 'core': '108.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [6, 15552, 10368, 16056, 36, 12096, 18144, 432, 5712], 'label': '31104.fx.18.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.m1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.m1', 'subgroup_fusion': None, 'weyl_group': '3456.gu'}
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id: 186248436
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.df1', '48.s1', '48.t1', '72.bl1'], 'contains': ['288.bl1', '432.gp1', '432.gq1', '432.gr1', '432.gs1', '432.gx1', '432.gy1', '576.cj1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [1, 15552, 18648, 76, 10368, 22752], 'label': '31104.fx.144.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '144.cv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cv1', 'subgroup_fusion': None, 'weyl_group': '1296.2940'}
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id: 186248437
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dg1', '48.t1'], 'contains': ['288.bt1', '432.gt1', '432.gy1', '432.ha1', '432.hb1', '432.hc1', '432.hh1', '432.hi1', '432.hj1', '432.hj2', '576.ck1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [1, 18144, 18216, 508, 5712, 12384], 'label': '31104.fx.144.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.cw1', 'old_label': '144.cw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cw1', 'subgroup_fusion': None, 'weyl_group': '216.165'}
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id: 186248438
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dg1', '48.t1'], 'contains': ['288.bv1', '432.gv1', '432.gx1', '432.gz1', '432.hd1', '432.he1', '432.hh1', '432.hi1', '432.hj1', '432.hj2', '576.ck1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [1, 15552, 18648, 76, 5712, 12384], 'label': '31104.fx.144.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.cx1', 'old_label': '144.cx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cx1', 'subgroup_fusion': None, 'weyl_group': '216.165'}
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id: 186248439
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dh1', '48.t1', '72.bh1'], 'contains': ['288.bw1', '432.gu1', '432.gv1', '432.gx1', '432.hb1', '432.hc1', '432.hf1', '432.hg1', '576.cl1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [1, 15552, 18648, 20812, 5712, 12384], 'label': '31104.fx.144.cy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bh1', 'old_label': '144.cy1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cy1', 'subgroup_fusion': None, 'weyl_group': '432.747'}
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id: 186248440
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dh1', '48.t1', '72.bi1'], 'contains': ['288.by1', '432.gt1', '432.gw1', '432.gy1', '432.hd1', '432.he1', '432.hf1', '432.hg1', '576.cl1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [1, 18144, 18216, 21244, 5712, 12384], 'label': '31104.fx.144.cz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bi1', 'old_label': '144.cz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cz1', 'subgroup_fusion': None, 'weyl_group': '432.747'}
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id: 186248441
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.u1', '72.a1', '72.bw1', '72.bx1', '72.ce1', '72.cf1', '72.cj1', '72.ck1'], 'contains': ['288.a1', '288.bb1', '288.bi1', '432.hk1', '432.hn1', '432.ho1', '432.hp1', '432.hq1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [18144, 2016, 10368, 3096, 15552, 12096], 'label': '31104.fx.144.da1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '144.da1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.da1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 186248442
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.df1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.u1', '72.bt1', '72.by1', '72.cb1', '72.ci1', '72.cl1', '72.cm1', '72.cx1'], 'contains': ['288.bk1', '432.hl1', '432.hn1', '432.hr1', '432.hs1', '432.ht1', '576.c1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [3024, 18144, 18216, 10924, 22752, 12384], 'label': '31104.fx.144.db1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '144.db1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.db1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186248443
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.df1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.u1', '72.bz1', '72.cn1', '72.cy1'], 'contains': ['288.bn1', '432.hm1', '432.hn1', '432.hu1', '432.hv1', '432.hw1', '576.d1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [16056, 15552, 18648, 14400, 29404, 2016], 'label': '31104.fx.144.dc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.q1', 'old_label': '144.dc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dc1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
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id: 186248444
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.df1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.u1', '72.bu1', '72.ca1', '72.cc1', '72.cg1', '72.co1', '72.cp1', '72.da1'], 'contains': ['288.bq1', '432.ho1', '432.hs1', '432.hu1', '576.e1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [504, 18144, 72, 556, 12096, 12384], 'label': '31104.fx.144.dd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '144.dd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dd1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186248445
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.df1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.u1', '72.bv1', '72.cd1', '72.da1'], 'contains': ['288.bq1', '432.hp1', '432.hs1', '432.hv1', '576.f1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [16056, 18144, 72, 556, 12096, 12384], 'label': '31104.fx.144.de1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.k1', 'old_label': '144.de1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.de1', 'subgroup_fusion': None, 'weyl_group': '72.44'}
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id: 186248446
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '18.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.a1', '6.c1', '9.c1'], 'contains': ['36.b1', '36.bo1', '36.ck1', '54.s1', '54.t1', '54.bc1', '72.ee1'], 'core': '36.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [19135, 15552, 10368, 16056, 36, 22752, 2592, 18576, 25852], 'label': '31104.fx.18.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '18.n1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.n1', 'subgroup_fusion': None, 'weyl_group': '10368.fj'}
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id: 186248447
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.df1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.u1', '72.ch1', '72.cq1', '72.db1'], 'contains': ['288.bs1', '432.ho1', '432.ht1', '432.hv1', '576.g1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [504, 18144, 72, 12096, 10924, 12384], 'label': '31104.fx.144.df1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.v1', 'old_label': '144.df1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.df1', 'subgroup_fusion': None, 'weyl_group': '72.42'}
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id: 186248448
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.df1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.u1', '72.db1'], 'contains': ['288.bs1', '432.hp1', '432.ht1', '432.hu1', '432.hv1', '576.h1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [16056, 18144, 72, 12096, 10924, 12384], 'label': '31104.fx.144.dg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.n1', 'old_label': '144.dg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dg1', 'subgroup_fusion': None, 'weyl_group': '36.11'}
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id: 186248449
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.e1', '72.dg1', '72.dh1', '72.di1', '72.dj1', '72.eh1', '72.ei1'], 'contains': ['288.cb1', '288.cc1', '288.cd1', '288.dg1', '288.dn1', '432.hx1', '432.hy1', '432.hz1', '432.ia1'], 'core': '576.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [26047, 10368, 22752, 36, 18576, 12096], 'label': '31104.fx.144.dh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '144.dh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dh1', 'subgroup_fusion': None, 'weyl_group': '432.759'}
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id: 186248450
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.f1', '72.dg1', '72.di1', '72.dk1', '72.ej1'], 'contains': ['288.cb1', '288.ce1', '288.ci1', '288.dh1', '288.ee1', '432.ib1', '432.ic1', '432.id1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1, 10368, 22752, 36, 2592, 12096], 'label': '31104.fx.144.di1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '144.di1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.di1', 'subgroup_fusion': None, 'weyl_group': '432.759'}
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id: 186248451
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.e1', '72.dg1', '72.dh1', '72.dk1', '72.dl1', '72.eh1', '72.ek1'], 'contains': ['288.cb1', '288.cj1', '288.cl1', '432.ie1', '432.if1', '432.ig1', '432.ii1'], 'core': '576.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [10855, 10368, 22752, 36, 18576, 12096], 'label': '31104.fx.144.dj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '144.dj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dj1', 'subgroup_fusion': None, 'weyl_group': '432.759'}
-
id: 186248452
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.g1', '72.dh1', '72.dj1', '72.dl1', '72.ej1'], 'contains': ['288.cb1', '288.ck1', '288.cm1', '432.ih1', '432.ij1', '432.ik1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [15985, 10368, 22752, 36, 2592, 12096], 'label': '31104.fx.144.dk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '144.dk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dk1', 'subgroup_fusion': None, 'weyl_group': '432.759'}
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id: 186248453
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.i1', '72.di1', '72.dm1', '72.do1', '72.ds1', '72.en1', '72.eq1'], 'contains': ['288.cc1', '288.cd1', '288.ce1', '288.dk1', '432.il1', '432.iu1', '432.iz1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [26485, 10368, 12096, 12138, 18576, 22752], 'label': '31104.fx.144.dl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '144.dl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dl1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186248454
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.j1', '72.do1', '72.dp1', '72.ds1', '72.dt1', '72.ei1', '72.em1'], 'contains': ['288.cc1', '288.cd1', '288.ch1', '288.dn1', '432.in1', '432.iv1', '432.iw1', '432.ix1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [26047, 10368, 22752, 2628, 18576, 12096], 'label': '31104.fx.144.dm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '144.dm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dm1', 'subgroup_fusion': None, 'weyl_group': '432.759'}
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id: 186248455
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.k1', '72.dj1', '72.dn1', '72.dp1', '72.dt1', '72.en1', '72.eq1'], 'contains': ['288.cc1', '288.cd1', '288.ck1', '432.im1', '432.iy1', '432.ja1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [29077, 10368, 12096, 12138, 22752, 18576], 'label': '31104.fx.144.dn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '144.dn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dn1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186248456
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.i1', '72.dg1', '72.dq1', '72.ds1', '72.du1', '72.eo1', '72.eq1'], 'contains': ['288.cc1', '288.ce1', '288.cl1', '432.io1', '432.jb1', '432.jc1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [26485, 10368, 12096, 14802, 22752, 18576], 'label': '31104.fx.144.do1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '144.do1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.do1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186248457
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '18.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1', '6.f1'], 'contains': ['36.y1', '36.ba1', '36.be1', '36.bi1', '36.bn1', '36.cn1', '36.de1', '54.u1', '54.x1', '54.y1', '54.bd1', '72.bj1'], 'core': '216.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1, 18144, 10924, 2016, 36, 15552, 18216, 10368, 18576], 'label': '31104.fx.18.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '18.o1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.o1', 'subgroup_fusion': None, 'weyl_group': '864.4691'}
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id: 186248458
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.e1', '72.dm1', '72.dn1', '72.du1', '72.dv1', '72.em1', '72.et1'], 'contains': ['288.cc1', '288.cg1', '288.cl1', '432.ip1', '432.jd1', '432.je1', '432.jf1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [10855, 10368, 22752, 18684, 18576, 12096], 'label': '31104.fx.144.dp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '144.dp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dp1', 'subgroup_fusion': None, 'weyl_group': '432.759'}
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id: 186248459
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.j1', '72.dq1', '72.dr1', '72.ds1', '72.dt1', '72.eh1', '72.et1'], 'contains': ['288.cc1', '288.ch1', '288.cl1', '432.iq1', '432.jg1', '432.jh1', '432.ji1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [10855, 10368, 22752, 16092, 18576, 12096], 'label': '31104.fx.144.dq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '144.dq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dq1', 'subgroup_fusion': None, 'weyl_group': '432.759'}
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id: 186248460
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.l1', '72.dg1', '72.dm1', '72.dp1', '72.dr1', '72.ep1', '72.ew1'], 'contains': ['288.cc1', '288.ci1', '288.cj1', '432.ir1', '432.jj1', '432.jk1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [5713, 10368, 22752, 14730, 12096, 18576], 'label': '31104.fx.144.dr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '144.dr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dr1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186248461
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.m1', '72.dh1', '72.dn1', '72.do1', '72.dq1', '72.ep1', '72.ew1'], 'contains': ['288.cc1', '288.cj1', '288.cm1', '432.is1', '432.jl1', '432.jn1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [8305, 10368, 22752, 14730, 12096, 18576], 'label': '31104.fx.144.ds1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '144.ds1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ds1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186248462
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.k1', '72.dh1', '72.dr1', '72.dt1', '72.dv1', '72.eo1', '72.eq1'], 'contains': ['288.cc1', '288.ck1', '288.cl1', '432.it1', '432.jm1', '432.jo1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [29077, 10368, 12096, 14802, 22752, 18576], 'label': '31104.fx.144.dt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '144.dt1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dt1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186248463
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.l1', '72.di1', '72.dt1', '72.du1', '72.ew1'], 'contains': ['288.cc1', '288.ci1', '288.do1', '432.jp1', '432.jr1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [5713, 10368, 22752, 12138, 18576, 12096], 'label': '31104.fx.144.du1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '144.du1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.du1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186248464
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.dv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.m1', '72.dj1', '72.ds1', '72.dv1', '72.ew1'], 'contains': ['288.cc1', '288.cm1', '432.jq1', '432.js1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [8305, 10368, 22752, 12138, 12096, 18576], 'label': '31104.fx.144.dv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '144.dv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dv1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186248465
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.i1', '72.dg1', '72.do1', '72.dw1', '72.dy1', '72.en1', '72.ez1'], 'contains': ['288.cd1', '288.ce1', '288.cj1', '432.jt1', '432.ju1', '432.kj1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [26485, 10368, 12096, 14730, 22752, 18576], 'label': '31104.fx.144.dw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '144.dw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dw1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186248466
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.dx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.e1', '72.dm1', '72.dn1', '72.dy1', '72.dz1', '72.em1', '72.fc1'], 'contains': ['288.cd1', '288.cg1', '288.cj1', '432.jv1', '432.jw1', '432.jx1', '432.kk1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [26047, 10368, 22752, 18684, 18576, 12096], 'label': '31104.fx.144.dx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '144.dx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dx1', 'subgroup_fusion': None, 'weyl_group': '432.759'}
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id: 186248467
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.j1', '72.do1', '72.dp1', '72.dw1', '72.dx1', '72.eh1', '72.fc1'], 'contains': ['288.cd1', '288.ch1', '288.cj1', '432.jy1', '432.jz1', '432.ka1', '432.kl1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [26047, 10368, 22752, 16092, 18576, 12096], 'label': '31104.fx.144.dy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '144.dy1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dy1', 'subgroup_fusion': None, 'weyl_group': '432.759'}
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id: 186248468
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '18.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.d1', '6.g1', '9.c1'], 'contains': ['36.bo1', '36.co1', '36.df1', '54.v1', '54.w1', '54.z1', '54.bd1', '72.bl1', '72.ef1'], 'core': '72.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1, 15552, 10368, 16056, 36, 12384, 2592, 18576, 76], 'label': '31104.fx.18.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '18.p1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.p1', 'subgroup_fusion': None, 'weyl_group': '3456.de'}
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id: 186248469
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.n1', '72.dg1', '72.dm1', '72.dt1', '72.dx1', '72.fa1', '72.ff1'], 'contains': ['288.cd1', '288.ci1', '288.cl1', '432.kb1', '432.kc1', '432.km1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [5713, 10368, 22752, 2598, 18576, 12096], 'label': '31104.fx.144.dz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '144.dz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dz1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
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id: 186248470
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.k1', '72.dh1', '72.dp1', '72.dx1', '72.dz1', '72.en1', '72.ez1'], 'contains': ['288.cd1', '288.cj1', '288.ck1', '432.kd1', '432.kf1', '432.kn1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [29077, 10368, 12096, 14730, 22752, 18576], 'label': '31104.fx.144.ea1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '144.ea1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ea1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
-
id: 186248471
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.eb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.o1', '72.dh1', '72.dn1', '72.ds1', '72.dw1', '72.fa1', '72.ff1'], 'contains': ['288.cd1', '288.cl1', '288.cm1', '432.ke1', '432.kg1', '432.ko1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [8305, 10368, 22752, 2598, 18576, 12096], 'label': '31104.fx.144.eb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '144.eb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.eb1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
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id: 186248472
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.ec1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.n1', '72.di1', '72.dp1', '72.dy1', '72.ff1'], 'contains': ['288.cd1', '288.ci1', '288.eb1', '432.kh1', '432.kp1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [5713, 10368, 22752, 6, 18576, 12096], 'label': '31104.fx.144.ec1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '144.ec1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ec1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
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id: 186248473
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.ed1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.o1', '72.dj1', '72.do1', '72.dz1', '72.ff1'], 'contains': ['288.cd1', '288.cm1', '432.ki1', '432.kq1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [8305, 10368, 22752, 6, 18576, 12096], 'label': '31104.fx.144.ed1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '144.ed1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ed1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
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id: 186248474
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.ee1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.f1', '72.dm1', '72.du1', '72.dy1', '72.fg1'], 'contains': ['288.ce1', '288.cg1', '288.ci1', '288.ed1', '432.kr1', '432.ku1', '432.kv1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1, 10368, 22752, 15588, 2592, 12096], 'label': '31104.fx.144.ee1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '144.ee1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ee1', 'subgroup_fusion': None, 'weyl_group': '432.759'}
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id: 186248475
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.ef1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.q1', '72.do1', '72.dq1', '72.ds1', '72.dw1', '72.ej1', '72.fg1'], 'contains': ['288.ce1', '288.ch1', '288.cm1', '432.ks1', '432.kw1', '432.kw2', '432.kx1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [15985, 10368, 22752, 468, 2592, 12096], 'label': '31104.fx.144.ef1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '144.ef1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ef1', 'subgroup_fusion': None, 'weyl_group': '432.759'}
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id: 186248476
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.eg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.i1', '72.dk1', '72.dm1', '72.dq1', '72.dw1', '72.eo1', '72.ez1'], 'contains': ['288.ce1', '288.cj1', '288.cl1', '432.kt1', '432.ky1', '432.kz1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [26485, 22752, 12096, 78, 10368, 18576], 'label': '31104.fx.144.eg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '144.eg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.eg1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186248477
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.eh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.g1', '72.dn1', '72.dv1', '72.dz1', '72.fg1'], 'contains': ['288.cg1', '288.ck1', '288.cm1', '432.la1', '432.lb1', '432.lc1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [15985, 10368, 22752, 15588, 2592, 12096], 'label': '31104.fx.144.eh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '144.eh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.eh1', 'subgroup_fusion': None, 'weyl_group': '432.759'}
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id: 186248478
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.ei1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.u1', '72.dp1', '72.dr1', '72.dt1', '72.dx1', '72.ej1', '72.fg1'], 'contains': ['288.ch1', '288.ci1', '288.ck1', '432.ld1', '432.ld2', '432.le1', '432.lf1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1, 10368, 22752, 468, 2592, 12096], 'label': '31104.fx.144.ei1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '144.ei1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ei1', 'subgroup_fusion': None, 'weyl_group': '432.759'}
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id: 186248479
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '18.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.g1', '9.b1'], 'contains': ['36.bm1', '36.cr1', '36.cx1', '54.w1', '54.be1', '72.bm1', '72.eg1'], 'core': '216.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1, 15552, 10368, 16056, 36, 12096, 2592, 432, 5712], 'label': '31104.fx.18.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.q1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.q1', 'subgroup_fusion': None, 'weyl_group': '3456.gu'}
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id: 186248480
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.j1', '72.dq1', '72.dr1', '72.dw1', '72.dx1', '72.ek1', '72.em1'], 'contains': ['288.ch1', '288.cj1', '288.cl1', '432.lg1', '432.lh1', '432.li1', '432.lj1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [10855, 10368, 22752, 2628, 18576, 12096], 'label': '31104.fx.144.ej1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '144.ej1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ej1', 'subgroup_fusion': None, 'weyl_group': '432.759'}
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id: 186248481
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.l1', '72.dk1', '72.dx1', '72.dy1', '72.ep1'], 'contains': ['288.ci1', '288.cj1', '432.lk1', '432.lm1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [5713, 10368, 22752, 12210, 12096, 18576], 'label': '31104.fx.144.ek1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '144.ek1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ek1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186248482
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.el1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.n1', '72.dk1', '72.dr1', '72.du1', '72.fa1'], 'contains': ['288.ci1', '288.cl1', '432.ll1', '432.ln1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [5713, 10368, 22752, 78, 18576, 12096], 'label': '31104.fx.144.el1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '144.el1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.el1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
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id: 186248483
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.em1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.k1', '72.dl1', '72.dn1', '72.dr1', '72.dx1', '72.eo1', '72.ez1'], 'contains': ['288.cj1', '288.ck1', '288.cl1', '432.lo1', '432.lp1', '432.ls1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [29077, 22752, 12096, 78, 10368, 18576], 'label': '31104.fx.144.em1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '144.em1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.em1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186248484
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.en1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.m1', '72.dl1', '72.dw1', '72.dz1', '72.ep1'], 'contains': ['288.cj1', '288.cm1', '432.lq1', '432.lt1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [8305, 10368, 22752, 12210, 12096, 18576], 'label': '31104.fx.144.en1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '144.en1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.en1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186248485
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.eo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.o1', '72.dl1', '72.dq1', '72.dv1', '72.fa1'], 'contains': ['288.cl1', '288.cm1', '432.lr1', '432.lu1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [8305, 10368, 22752, 78, 18576, 12096], 'label': '31104.fx.144.eo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '144.eo1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.eo1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
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id: 186248486
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.ep1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.bm1', '48.v1', '72.ea1', '72.ec1', '72.eg1'], 'contains': ['288.cn1', '432.lw1', '432.lz1', '576.l1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [36, 22752, 12096, 20812, 2664, 18576], 'label': '31104.fx.144.ep1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.di1', 'old_label': '144.ep1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ep1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
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id: 186248487
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.eq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.bm1', '48.v1', '72.ed1'], 'contains': ['288.co1', '432.lw1', '432.ma1', '576.l1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [36, 10368, 12096, 5712, 15624, 432], 'label': '31104.fx.144.eq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.ed1', 'old_label': '144.eq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.eq1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
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id: 186248488
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.er1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.bo1', '48.v1', '72.eb1', '72.ee1', '72.ef1'], 'contains': ['288.cs1', '432.lv1', '432.lw1', '432.lx1', '432.mb1', '576.n1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [36, 10368, 12384, 76, 2664, 18576], 'label': '31104.fx.144.er1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.dj1', 'old_label': '144.er1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.er1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
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id: 186248489
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.es1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.v1', '72.w1', '72.eh1', '72.ei1', '72.ej1', '72.ek1'], 'contains': ['288.cb1', '288.ch1', '288.cr1', '432.ly1', '432.lz1', '432.ma1', '432.mb1', '432.mc1'], 'core': '576.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [36, 10368, 22752, 16056, 432, 12096], 'label': '31104.fx.144.es1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '144.es1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.es1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
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id: 186248490
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '18.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1'], 'contains': ['36.z1', '36.bb1', '36.bg1', '36.bh1', '36.bp1', '36.cu1', '36.da1', '54.y1', '54.bf1', '72.bn1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [20737, 18144, 556, 1728, 36, 15552, 18216, 12384, 18576], 'label': '31104.fx.18.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.r1', 'old_label': '18.r1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.r1', 'subgroup_fusion': None, 'weyl_group': '864.4000'}
-
id: 186248491
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.et1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.bq1', '48.w1', '72.ea1', '72.el1', '72.ex1'], 'contains': ['288.cn1', '432.me1', '432.mf1', '432.mg1', '576.p1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [12138, 18576, 2664, 20812, 12096, 22752], 'label': '31104.fx.144.et1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.di1', 'old_label': '144.et1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.et1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186248492
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.eu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.gc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.x1', '72.x1', '72.eh1', '72.em1', '72.en1', '72.eo1', '72.ep1', '72.ew1'], 'contains': ['288.cc1', '288.cj1', '288.cr1', '432.md1', '432.mh1', '432.mi1', '432.mk1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [12138, 10368, 16056, 432, 12096, 22752], 'label': '31104.fx.144.eu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '144.eu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.eu1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186248493
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.ev1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.gc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.w1', '72.x1', '72.ei1', '72.eq1', '72.et1', '72.ew1'], 'contains': ['288.cc1', '288.cr1', '432.me1', '432.ml1', '432.mo1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [12138, 10368, 22752, 16056, 18576, 12096], 'label': '31104.fx.144.ev1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '144.ev1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ev1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
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id: 186248494
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.ew1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.bt1', '48.w1', '72.eb1', '72.er1', '72.ey1'], 'contains': ['288.cs1', '432.mf1', '432.mm1', '432.mo1', '576.s1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [12138, 10368, 18576, 76, 22752, 2664], 'label': '31104.fx.144.ew1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.x1', 'old_label': '144.ew1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ew1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
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id: 186248495
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.ex1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.bu1', '48.w1', '72.es1'], 'contains': ['288.ct1', '432.mg1', '432.mn1', '432.mo1', '576.t1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [17371, 22752, 2592, 29904, 10368, 15984], 'label': '31104.fx.144.ex1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.t1', 'old_label': '144.ex1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ex1', 'subgroup_fusion': None, 'weyl_group': '432.747'}
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id: 186248496
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.ey1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.bv1', '48.x1', '72.ec1', '72.ev1', '72.ex1'], 'contains': ['288.cn1', '432.mh1', '432.mp1', '576.u1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [17371, 18576, 16056, 12096, 7780, 22752], 'label': '31104.fx.144.ey1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.x1', 'old_label': '144.ey1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ey1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
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id: 186248497
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.ez1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.bv1', '48.x1', '72.ed1'], 'contains': ['288.co1', '432.mi1', '432.mp1', '576.u1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [17371, 15984, 15624, 12096, 23836, 22752], 'label': '31104.fx.144.ez1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.r1', 'old_label': '144.ez1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ez1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
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id: 186248498
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.fa1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.b1', '48.x1', '72.ee1', '72.eu1', '72.ey1'], 'contains': ['288.cs1', '432.mj1', '432.mk1', '432.mp1', '576.x1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [12138, 432, 16056, 22752, 21192, 10368], 'label': '31104.fx.144.fa1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.x1', 'old_label': '144.fa1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fa1', 'subgroup_fusion': None, 'weyl_group': '864.4000'}
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id: 186248499
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.fb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.ca1', '48.y1', '72.eb1', '72.eu1', '72.fb1'], 'contains': ['288.cs1', '432.mq1', '432.my1', '432.mz1', '432.na1', '576.ba1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [26047, 10368, 2592, 5712, 22752, 15984], 'label': '31104.fx.144.fb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.dj1', 'old_label': '144.fb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fb1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
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id: 186248500
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.fc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.cb1', '48.z1', '72.ec1', '72.el1', '72.fd1'], 'contains': ['288.cn1', '432.mr1', '432.mt1', '432.mv1', '576.bb1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [6, 2592, 18576, 5712, 12096, 10368], 'label': '31104.fx.144.fc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.di1', 'old_label': '144.fc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fc1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186248501
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '3.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['6.a1', '6.e1', '6.g1', '6.h1', '6.i1', '6.l1', '6.n1', '9.b1', '9.c1', '9.d1', '12.x1'], 'core': '6.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [5713, 18576, 12096, 10368, 2592, 6, 15628, 2664, 22752, 15552, 36], 'label': '31104.fx.3.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '3.b1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.b1', 'subgroup_fusion': None, 'weyl_group': '10368.je'}
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id: 186248502
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '18.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.a1', '6.e1', '9.d1'], 'contains': ['36.a1', '36.g1', '36.i1', '36.l1', '36.p1', '36.bs1', '36.cj1', '54.ba1', '54.bb1', '54.bc1'], 'core': '36.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [26047, 10368, 18576, 2592, 36, 15552, 22752, 12096, 16056], 'label': '31104.fx.18.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '18.s1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.s1', 'subgroup_fusion': None, 'weyl_group': '2592.jb'}
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id: 186248503
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.fd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.cb1', '48.z1', '72.ed1'], 'contains': ['288.co1', '432.ms1', '432.mt1', '432.mv2', '576.bb1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [6, 432, 16056, 5712, 12096, 10368], 'label': '31104.fx.144.fd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.ed1', 'old_label': '144.fd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fd1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
-
id: 186248504
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.fe1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.cd1', '48.z1', '72.fe1'], 'contains': ['288.cp1', '432.mr1', '432.mu1', '432.mv2', '576.bd1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [6, 2592, 18576, 28464, 12096, 10368], 'label': '31104.fx.144.fe1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.fe1', 'old_label': '144.fe1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fe1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
-
id: 186248505
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.ff1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.cd1', '48.z1'], 'contains': ['288.cq1', '432.ms1', '432.mu1', '432.mv1', '432.mv2', '576.bd1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [26047, 15984, 15624, 3100, 12096, 22752], 'label': '31104.fx.144.ff1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.ff1', 'old_label': '144.ff1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ff1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
-
id: 186248506
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.fg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ep1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.z1', '72.y1', '72.eh1', '72.em1', '72.eq1', '72.ez1', '72.fa1', '72.ff1'], 'contains': ['288.cd1', '288.cl1', '288.cr1', '432.mr1', '432.ms1', '432.mw1', '432.nb1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [26047, 10368, 12096, 16056, 22752, 18576], 'label': '31104.fx.144.fg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '144.fg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fg1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186248507
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.fh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.ck1', '48.z1', '72.ee1', '72.er1', '72.fb1'], 'contains': ['288.cs1', '432.mt1', '432.mu1', '432.mw1', '432.nc1', '576.bk1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [6, 432, 16056, 10368, 21192, 22752], 'label': '31104.fx.144.fh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.dj1', 'old_label': '144.fh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fh1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
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id: 186248508
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.fi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.cl1', '48.z1', '72.es1'], 'contains': ['288.ct1', '432.mv1', '432.mv2', '432.mw1', '432.nd1', '576.bl1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [26047, 18576, 16056, 22752, 20452, 10368], 'label': '31104.fx.144.fi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.es1', 'old_label': '144.fi1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fi1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
-
id: 186248509
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.fj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.cc1', '48.y1', '72.ea1', '72.ev1', '72.fd1'], 'contains': ['288.cn1', '432.my1', '432.ne1', '576.bc1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [26047, 10368, 12096, 5712, 15984, 2592], 'label': '31104.fx.144.fj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.x1', 'old_label': '144.fj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fj1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
-
id: 186248510
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.fk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.ce1', '48.y1', '72.fe1'], 'contains': ['288.cp1', '432.mz1', '432.ne1', '576.be1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [6, 22752, 12096, 76, 2664, 18576], 'label': '31104.fx.144.fk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.w1', 'old_label': '144.fk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fk1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
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id: 186248511
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.fl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ep1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.y1', '72.y1', '72.ei1', '72.en1', '72.fc1', '72.ff1'], 'contains': ['288.cd1', '288.cr1', '432.mx1', '432.na1', '432.ne1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [6, 22752, 12096, 16056, 18576, 10368], 'label': '31104.fx.144.fl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '144.fl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fl1', 'subgroup_fusion': None, 'weyl_group': '864.4000'}
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id: 186248512
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.fm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.ba1', '72.z1', '72.ej1', '72.en1', '72.eo1', '72.eq1', '72.ez1', '72.fg1'], 'contains': ['288.ce1', '288.ck1', '288.cr1', '432.nf1', '432.ng1', '432.nh1', '432.nl1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [10405, 1728, 2592, 18576, 22752, 10368], 'label': '31104.fx.144.fm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '144.fm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fm1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186248513
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '18.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1', '6.g1', '9.d1'], 'contains': ['36.a1', '36.h1', '36.j1', '36.t1', '36.v1', '36.bc1', '36.bd1', '36.bf1', '36.bj1', '36.cm1', '36.cz1', '54.bd1', '54.be1', '54.bf1'], 'core': '36.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1, 10368, 2592, 15552, 36, 18576, 22752, 12096, 16056], 'label': '31104.fx.18.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '18.t1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.t1', 'subgroup_fusion': None, 'weyl_group': '864.4406'}
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id: 186248514
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.fn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.co1', '48.ba1', '72.ef1', '72.er1', '72.eu1'], 'contains': ['288.cs1', '432.nf1', '432.ni1', '432.nj1', '432.nm1', '576.bo1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [10405, 2592, 18576, 22752, 10368, 16080], 'label': '31104.fx.144.fn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.dj1', 'old_label': '144.fn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fn1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
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id: 186248515
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.fo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.cq1', '48.ba1', '72.es1'], 'contains': ['288.ct1', '432.nf1', '432.nk1', '432.nk2', '432.nn1', '576.bq1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [10405, 2592, 432, 22752, 10368, 24268], 'label': '31104.fx.144.fo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.es1', 'old_label': '144.fo1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fo1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186248516
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.fp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.bj1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.cr1', '48.ba1', '72.eg1', '72.el1', '72.ev1'], 'contains': ['288.cn1', '432.nh1', '432.nj1', '432.nk1', '576.br1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [10405, 2592, 18576, 16080, 1728, 10368], 'label': '31104.fx.144.fp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.x1', 'old_label': '144.fp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fp1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186248517
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.fq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.w1', '72.ba1', '72.em1', '72.et1', '72.fc1', '72.fg1', '72.fh1'], 'contains': ['288.cf1', '288.cg1', '288.ch1', '288.cr1', '432.no1', '432.no2', '432.np1', '432.nq1', '432.nr1', '432.ns1', '432.ns2'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [18180, 22752, 10368, 16056, 18576, 12096], 'label': '31104.fx.144.fq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '144.fq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fq1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
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id: 186248518
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.fr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.cx1', '48.bb1', '72.eg1', '72.ex1', '72.fd1'], 'contains': ['288.cn1', '432.nu1', '432.nx1', '576.cb1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [1, 2592, 18576, 12096, 5712, 10368], 'label': '31104.fx.144.fr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.di1', 'old_label': '144.fr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fr1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
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id: 186248519
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.fs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.cy1', '48.bb1', '72.fe1'], 'contains': ['288.cp1', '432.nu1', '432.ny1', '576.cc1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [1, 2592, 18576, 12096, 28464, 10368], 'label': '31104.fx.144.fs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.fe1', 'old_label': '144.fs1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fs1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
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id: 186248520
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.ft1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.bb1', '72.bb1', '72.ej1', '72.ep1', '72.ew1', '72.fa1', '72.ff1', '72.fg1'], 'contains': ['288.ci1', '288.cm1', '288.cr1', '432.nt1', '432.nu1', '432.nv1', '432.nz1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1, 10368, 22752, 3024, 12096, 2592], 'label': '31104.fx.144.ft1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '144.ft1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ft1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186248521
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.fu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.df1', '48.bb1', '72.ef1', '72.ey1', '72.fb1'], 'contains': ['288.cs1', '432.nw1', '432.nx1', '432.ny1', '432.nz1', '432.oa1', '576.cj1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [1, 2592, 18576, 5712, 22752, 10368], 'label': '31104.fx.144.fu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.x1', 'old_label': '144.fu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fu1', 'subgroup_fusion': None, 'weyl_group': '2592.jb'}
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id: 186248522
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.fv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.gc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.x1', '72.bc1', '72.ek1', '72.ep1', '72.ez1', '72.fc1', '72.fh1'], 'contains': ['288.cj1', '288.cr1', '432.ob1', '432.oc1', '432.od1', '432.og1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [2179, 22752, 18576, 2592, 12096, 10368], 'label': '31104.fx.144.fv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '144.fv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fv1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186248523
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.fw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ep1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.y1', '72.be1', '72.ek1', '72.eo1', '72.et1', '72.fa1', '72.fh1'], 'contains': ['288.cl1', '288.cr1', '432.oe1', '432.oe2', '432.of1', '432.oh1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [10855, 10368, 12096, 2592, 22752, 18576], 'label': '31104.fx.144.fw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '144.fw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fw1', 'subgroup_fusion': None, 'weyl_group': '288.977'}
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id: 186248524
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '18.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.h1', '9.b1'], 'contains': ['36.bq1', '36.cb1', '36.cr1', '54.bg1', '54.bh1', '54.bi1', '72.el1'], 'core': '216.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [10405, 15552, 10368, 16056, 6, 1728, 2592, 432, 28176], 'label': '31104.fx.18.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.u1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.u1', 'subgroup_fusion': None, 'weyl_group': '1152.155790'}
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id: 186248525
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.fx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['9.a1', '48.bc1'], 'contains': ['288.cu1', '288.cv1', '288.cw1', '288.dj1', '288.dr1', '288.du1', '288.dx1', '432.oi1', '432.oj1', '432.ok1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [1, 10368, 16080, 24198, 36, 10228], 'label': '31104.fx.144.fx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fx1', 'old_label': '144.fx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fx1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
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id: 186248526
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.fy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.di1', '48.bd1'], 'contains': ['288.cy1', '288.da1', '288.de1', '288.di1', '288.dq1', '288.dt1', '288.dz1', '432.ok1', '432.ol1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [1, 10368, 12096, 6, 36, 5712], 'label': '31104.fx.144.fy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fy1', 'old_label': '144.fy1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fy1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
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id: 186248527
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.fz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.dj1', '48.bc1', '48.bd1'], 'contains': ['288.cz1', '288.db1', '288.dd1', '288.dl1', '288.dp1', '288.dv1', '288.dy1', '432.oj1', '432.ok1', '432.om1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [1, 10368, 22752, 24198, 36, 16080], 'label': '31104.fx.144.fz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fz1', 'old_label': '144.fz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fz1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
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id: 186248528
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.ga1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bd1', '72.di1'], 'contains': ['288.dg1', '288.dh1', '288.dk1', '288.do1', '288.eb1', '432.ol1', '432.om1'], 'core': '576.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [5713, 10368, 22752, 6, 36, 12096], 'label': '31104.fx.144.ga1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.di1', 'old_label': '144.ga1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ga1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
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id: 186248529
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '144.gb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.di1'], 'contains': ['288.dk1', '288.dn1', '288.do1', '288.eb1', '288.ee1', '432.on1', '432.oo1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [5713, 10368, 22752, 6, 18612, 12096], 'label': '31104.fx.144.gb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.di1', 'old_label': '144.gb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gb1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
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id: 186248530
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '162.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.a1', '54.c1', '81.c1'], 'contains': ['324.i1', '324.q1', '324.r1', '324.bb1', '324.bc1', '324.br1', '324.bs1', '486.a1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [21265, 18576, 15984, 24198, 22752, 36, 18648], 'label': '31104.fx.162.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '162.a1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.a1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
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id: 186248531
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '162.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.a1', '54.b1', '81.b1'], 'contains': ['324.j1', '324.t1', '324.v1', '324.bd1', '324.be1', '324.bt1', '324.bu1', '486.a1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [21265, 18576, 15984, 15558, 12096, 36, 18648], 'label': '31104.fx.162.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '162.b1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.b1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
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id: 186248532
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '162.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.d1', '81.b1'], 'contains': ['324.a1', '324.b1', '324.e1', '324.f1', '324.j1', '324.o1', '324.x1', '324.bf1', '324.bw1', '324.en1', '324.ep1', '324.et1', '324.eu1', '486.b1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [5713, 18576, 2592, 6, 12096, 36, 16056], 'label': '31104.fx.162.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '162.c1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.c1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
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id: 186248533
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '162.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.b1', '54.c1', '81.c1'], 'contains': ['324.l1', '324.p1', '324.r1', '324.bi1', '324.bj1', '324.bm1', '324.bn1', '486.a1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [21265, 18576, 15984, 24198, 10368, 36, 18648], 'label': '31104.fx.162.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '162.d1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.d1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
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id: 186248534
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '162.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.d1', '54.e1', '81.c1'], 'contains': ['324.c1', '324.d1', '324.g1', '324.h1', '324.i1', '324.l1', '324.m1', '324.w1', '324.bg1', '324.bk1', '324.bv1', '324.em1', '324.eo1', '324.eq1', '324.er1', '324.es1', '324.ev1', '324.ew1', '324.ex1', '486.b1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [5713, 18576, 2592, 24198, 10368, 36, 16056], 'label': '31104.fx.162.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '162.e1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.e1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
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id: 186248535
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '18.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.j1', '9.a1'], 'contains': ['36.br1', '36.bz1', '36.cs1', '54.bh1', '54.bj1', '54.bl1', '288.dj1'], 'core': '216.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [12133, 15552, 5712, 16056, 6, 20812, 18144, 18576, 10368], 'label': '31104.fx.18.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.v1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.v1', 'subgroup_fusion': None, 'weyl_group': '1152.157852'}
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id: 186248536
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '162.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.f1', '54.g1', '81.c1'], 'contains': ['324.m1', '324.p1', '324.q1', '324.bz1', '324.ca1', '324.ci1', '324.cj1', '486.c1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [5713, 18576, 15984, 8646, 22752, 36, 18648], 'label': '31104.fx.162.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '162.f1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.f1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
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id: 186248537
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '162.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.g1', '81.b1'], 'contains': ['324.o1', '324.t1', '324.cc1', '324.cg1', '324.ch1', '486.c1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [5713, 18576, 15984, 15558, 12096, 36, 18648], 'label': '31104.fx.162.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '162.g1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.g1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
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id: 186248538
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '162.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.h1', '54.i1', '81.c1'], 'contains': ['324.w1', '324.y1', '324.bc1', '324.bl1', '324.bn1', '324.bx1', '324.ca1', '486.d1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [21265, 18576, 15984, 8646, 22752, 15588, 18648], 'label': '31104.fx.162.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '162.h1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.h1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
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id: 186248539
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '162.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.h1', '54.j1', '81.b1'], 'contains': ['324.x1', '324.z1', '324.be1', '324.bp1', '324.bu1', '324.cb1', '324.cc1', '486.d1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [21265, 18576, 15984, 15558, 12096, 15588, 18648], 'label': '31104.fx.162.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '162.i1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.i1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
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id: 186248540
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '162.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.k1', '81.b1'], 'contains': ['324.z1', '324.bd1', '324.bf1', '324.cd1', '324.ch1', '486.e1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [5713, 18576, 15984, 15558, 12096, 15588, 18648], 'label': '31104.fx.162.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '162.j1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.j1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
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id: 186248541
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '162.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.i1', '54.j1', '81.c1'], 'contains': ['324.bg1', '324.bh1', '324.bj1', '324.bo1', '324.bs1', '324.bx1', '324.bz1', '486.d1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [21265, 18576, 15984, 8646, 10368, 15588, 18648], 'label': '31104.fx.162.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '162.k1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.k1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
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id: 186248542
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '162.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.k1', '54.l1', '81.c1'], 'contains': ['324.y1', '324.bb1', '324.bh1', '324.bi1', '324.bk1', '324.ce1', '324.cj1', '486.e1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [5713, 18576, 15984, 8646, 10368, 15588, 18648], 'label': '31104.fx.162.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '162.l1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.l1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
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id: 186248543
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '162.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.m1', '54.n1', '81.c1'], 'contains': ['324.bl1', '324.bm1', '324.bo1', '324.br1', '324.bv1', '324.ce1', '324.ci1', '486.f1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [5713, 18576, 15984, 24198, 22752, 15588, 18648], 'label': '31104.fx.162.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '162.m1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.m1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
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id: 186248544
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '162.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.n1', '81.b1'], 'contains': ['324.bp1', '324.bt1', '324.bw1', '324.cd1', '324.cg1', '486.f1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [5713, 18576, 15984, 6, 12096, 15588, 18648], 'label': '31104.fx.162.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '162.n1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.n1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
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id: 186248546
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '18.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.h1', '6.i1', '9.d1'], 'contains': ['36.k1', '36.m1', '36.q1', '36.u1', '36.bs1', '36.cj1', '36.cm1', '54.bg1', '54.bk1', '54.bm1'], 'core': '72.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [26485, 22752, 72, 2592, 6, 10368, 12096, 18576, 15552], 'label': '31104.fx.18.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '18.w1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.w1', 'subgroup_fusion': None, 'weyl_group': '576.7160'}
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id: 186248547
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '162.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.o1', '54.s1', '54.t1', '81.a1'], 'contains': ['324.df1', '324.do1', '324.du1', '486.g1', '648.ie1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [24198, 18144, 432, 36, 15552, 16080, 16056], 'label': '31104.fx.162.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '162.p1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.p1', 'subgroup_fusion': None, 'weyl_group': '576.8654'}
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id: 186248548
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '162.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.p1', '54.u1', '54.x1', '54.y1'], 'contains': ['324.ck1', '324.cl1', '324.cx1', '324.cz1', '324.de1', '324.ea1', '324.eh1', '486.h1', '648.dz1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [20737, 18216, 12940, 36, 18144, 18576, 15552], 'label': '31104.fx.162.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.q1', 'old_label': '162.q1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.q1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 186248549
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '162.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.p1', '54.v1', '54.w1', '54.z1', '81.a1'], 'contains': ['324.df1', '324.eb1', '324.ei1', '486.h1', '648.eb1', '648.if1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [20737, 2592, 432, 36, 15552, 16080, 16056], 'label': '31104.fx.162.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '162.r1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.r1', 'subgroup_fusion': None, 'weyl_group': '192.955'}
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id: 186248550
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '162.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.q1', '54.s1', '54.ba1', '54.bc1', '81.c1'], 'contains': ['324.i1', '324.p1', '324.y1', '324.bo1', '324.dg1', '324.dj1', '324.ds1', '486.g1'], 'core': '648.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [29503, 2592, 18576, 36, 10368, 16056, 15552], 'label': '31104.fx.162.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '162.s1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.s1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
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id: 186248551
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '162.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.ba1', '54.bb1', '81.b1'], 'contains': ['324.j1', '324.k1', '324.t1', '324.u1', '324.z1', '324.ba1', '324.bp1', '324.bq1', '324.di1', '324.dk1', '324.dt1', '486.g1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [6, 18576, 16056, 36, 12096, 18144, 15552], 'label': '31104.fx.162.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '162.t1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.t1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
-
id: 186248552
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '162.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.r1', '54.t1', '54.bb1', '54.bc1', '81.c1'], 'contains': ['324.l1', '324.q1', '324.bh1', '324.bl1', '324.dg1', '324.dn1', '324.dp1', '486.g1'], 'core': '648.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [24198, 18576, 16056, 36, 10368, 18144, 15552], 'label': '31104.fx.162.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '162.u1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.u1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
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id: 186248553
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '162.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.u1', '54.v1', '54.w1', '54.bd1', '54.be1', '81.c1'], 'contains': ['324.m1', '324.r1', '324.bx1', '324.ce1', '324.cm1', '324.cq1', '324.cu1', '324.db1', '324.dg1', '324.dx1', '324.ef1', '486.h1'], 'core': '648.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1, 15552, 2592, 36, 10368, 16056, 18576], 'label': '31104.fx.162.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '162.v1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.v1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186248554
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '162.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.x1', '54.y1', '54.z1', '54.bd1', '54.bf1'], 'contains': ['324.n1', '324.s1', '324.by1', '324.cf1', '324.cn1', '324.co1', '324.cr1', '324.cs1', '324.cv1', '324.cw1', '324.dc1', '324.dd1', '324.dh1', '324.dy1', '324.eg1', '486.h1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [20737, 15552, 2592, 36, 12384, 16056, 18576], 'label': '31104.fx.162.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.w1', 'old_label': '162.w1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.w1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186248555
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '162.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.be1', '54.bf1', '81.b1'], 'contains': ['324.o1', '324.v1', '324.cb1', '324.cd1', '324.cp1', '324.ct1', '324.cy1', '324.da1', '324.di1', '324.dz1', '324.ee1', '486.h1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [20737, 15552, 2592, 36, 1728, 16056, 18576], 'label': '31104.fx.162.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '162.x1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.x1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186248556
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '162.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.bg1', '54.bh1', '54.bi1', '54.bj1', '54.bk1', '81.c1'], 'contains': ['324.w1', '324.bb1', '324.bm1', '324.bz1', '324.dj1', '324.dp1', '324.dx1', '486.i1'], 'core': '648.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [26485, 2592, 72, 12138, 18576, 15552, 22752], 'label': '31104.fx.162.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '162.y1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.y1', 'subgroup_fusion': None, 'weyl_group': '64.202'}
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id: 186248557
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '18.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.h1', '6.j1', '9.c1'], 'contains': ['36.bt1', '36.ck1', '36.co1', '54.bh1', '54.bk1', '54.bn1', '72.er1'], 'core': '72.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [26485, 15552, 10368, 2664, 12138, 28012, 2592, 18576, 22752], 'label': '31104.fx.18.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '18.x1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.x1', 'subgroup_fusion': None, 'weyl_group': '1152.155790'}
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id: 186248558
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '162.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.bg1', '54.bm1', '81.b1'], 'contains': ['324.x1', '324.bd1', '324.bt1', '324.cc1', '324.dk1', '324.dt1', '324.dz1', '486.i1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [26485, 18576, 2592, 6, 12096, 15552, 72], 'label': '31104.fx.162.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '162.z1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.z1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
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id: 186248559
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '162.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.q1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.bh1', '54.bl1', '54.bn1', '81.a1'], 'contains': ['324.dl1', '324.du1', '324.eb1', '486.i1', '648.jf1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [12133, 2592, 432, 6, 15552, 5712, 16056], 'label': '31104.fx.162.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '162.ba1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.ba1', 'subgroup_fusion': None, 'weyl_group': '192.955'}
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id: 186248560
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '162.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.bi1', '54.bo1'], 'contains': ['324.dm1', '324.dw1', '324.ed1', '486.i1', '648.jg1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13861, 2592, 432, 6, 15552, 19536, 16056], 'label': '31104.fx.162.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bi1', 'old_label': '162.bb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.bb1', 'subgroup_fusion': None, 'weyl_group': '192.955'}
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id: 186248561
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '162.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.bp1', '81.b1'], 'contains': ['324.be1', '324.bf1', '324.cg1', '324.dk1', '324.ee1', '486.j1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [5713, 2592, 72, 12138, 18576, 15552, 12096], 'label': '31104.fx.162.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '162.bc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.bc1', 'subgroup_fusion': None, 'weyl_group': '64.202'}
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id: 186248562
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '162.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.q1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.bj1', '54.bl1', '54.bu1', '81.a1'], 'contains': ['324.do1', '324.dq1', '324.eb1', '486.i1', '648.jk1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [10405, 2592, 432, 12138, 15552, 16080, 16056], 'label': '31104.fx.162.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '162.bd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.bd1', 'subgroup_fusion': None, 'weyl_group': '192.955'}
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id: 186248563
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '162.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.bk1', '54.bm1', '54.bn1', '54.bo1', '54.bu1', '81.c1'], 'contains': ['324.bg1', '324.bi1', '324.br1', '324.ca1', '324.dn1', '324.ds1', '324.dx1', '486.i1'], 'core': '648.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [26485, 18576, 2592, 12138, 10368, 15552, 72], 'label': '31104.fx.162.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '162.be1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.be1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
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id: 186248564
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '162.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.bp1', '54.bq1', '54.br1', '54.bv1', '81.c1'], 'contains': ['324.bc1', '324.bj1', '324.bk1', '324.ci1', '324.dj1', '324.dn1', '324.ef1', '486.j1'], 'core': '648.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [5713, 18576, 2592, 12138, 22752, 15552, 72], 'label': '31104.fx.162.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '162.bf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.bf1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
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id: 186248565
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '162.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.bq1', '54.bs1', '54.bt1', '54.bv1', '81.a1'], 'contains': ['324.dl1', '324.do1', '324.ei1', '486.j1', '648.jq1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1, 2592, 432, 12138, 15552, 5712, 16056], 'label': '31104.fx.162.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '162.bg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.bg1', 'subgroup_fusion': None, 'weyl_group': '192.955'}
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id: 186248566
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '162.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.bw1', '54.bx1', '54.by1', '54.cd1', '54.ce1', '81.c1'], 'contains': ['324.bn1', '324.bs1', '324.bv1', '324.cj1', '324.dp1', '324.ds1', '324.ef1', '486.k1'], 'core': '648.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [5713, 18576, 2592, 6, 10368, 15552, 72], 'label': '31104.fx.162.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '162.bh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.bh1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
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id: 186248567
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '162.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.bw1', '54.bz1', '54.cb1', '54.cd1', '81.a1'], 'contains': ['324.dq1', '324.du1', '324.ei1', '486.k1', '648.kc1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1, 2592, 432, 6, 15552, 5712, 16056], 'label': '31104.fx.162.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '162.bi1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.bi1', 'subgroup_fusion': None, 'weyl_group': '192.955'}
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id: 186248568
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '18.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.h1', '6.k1'], 'contains': ['36.bu1', '36.cl1', '36.cq1', '54.bi1', '54.bk1', '54.bo1', '72.es1'], 'core': '216.b1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [26485, 15552, 10368, 2664, 12138, 29452, 2592, 18576, 22752], 'label': '31104.fx.18.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.y1', 'old_label': '18.y1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.y1', 'subgroup_fusion': None, 'weyl_group': '576.5126'}
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id: 186248569
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '162.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.bx1', '54.ca1', '54.cb1', '54.cc1', '54.cd1'], 'contains': ['324.dr1', '324.dv1', '324.ek1', '486.k1', '648.kd1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [5713, 2592, 18576, 6, 15552, 15628, 2664], 'label': '31104.fx.162.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.bj1', 'old_label': '162.bj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.bj1', 'subgroup_fusion': None, 'weyl_group': '192.955'}
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id: 186248570
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '162.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.ce1', '81.b1'], 'contains': ['324.bu1', '324.bw1', '324.ch1', '324.dt1', '324.ee1', '486.k1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [5713, 18576, 2592, 6, 12096, 15552, 72], 'label': '31104.fx.162.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '162.bk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.bk1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
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id: 186248571
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '192.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.df1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.u1', '96.a1', '96.b1', '96.c1', '96.d1', '96.e1', '96.f1', '96.g1'], 'contains': ['384.a1', '576.b1', '576.c1', '576.d1', '576.e1', '576.f1', '576.g1', '576.h1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [3096, 12384, 10924, 12096, 10368], 'label': '31104.fx.192.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.d1', 'old_label': '192.a1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 186248572
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '192.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.r1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1', '64.a1', '96.o1', '96.p1'], 'contains': ['384.d1', '576.j1', '576.k1', '576.m1', '576.n1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [36, 10368, 18580, 5712, 12384], 'label': '31104.fx.192.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bc1', 'old_label': '192.b1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.b1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186248573
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '192.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1', '64.a1', '96.a1', '96.s1'], 'contains': ['384.a1', '576.a1', '576.m1', '576.o1'], 'core': '576.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [36, 10368, 10924, 12096, 2016], 'label': '31104.fx.192.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1', 'old_label': '192.c1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.c1', 'subgroup_fusion': None, 'weyl_group': '972.456'}
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id: 186248574
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '192.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.h1', '48.v1', '64.a1', '96.q1', '96.r1', '96.t1'], 'contains': ['384.b1', '576.a1', '576.l1', '576.n1'], 'core': '576.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [36, 10368, 5712, 12096, 22752], 'label': '31104.fx.192.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.d1', 'old_label': '192.d1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.d1', 'subgroup_fusion': None, 'weyl_group': '1944.2342'}
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id: 186248575
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '192.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.w1', '64.b1', '96.q1', '96.u1', '96.y1'], 'contains': ['384.b1', '576.p1', '576.r1', '576.s1', '576.t1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [14802, 10368, 76, 12096, 22752], 'label': '31104.fx.192.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bd1', 'old_label': '192.e1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.e1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
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id: 186248576
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '192.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.x1', '64.b1', '96.r1', '96.v1', '96.y1'], 'contains': ['384.b1', '576.r1', '576.u1', '576.x1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [17371, 22752, 12096, 10368, 23836], 'label': '31104.fx.192.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.d1', 'old_label': '192.f1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.f1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
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id: 186248577
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '192.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.c1', '64.b1', '96.o1', '96.w1', '96.z1'], 'contains': ['384.d1', '576.q1', '576.s1', '576.v1', '576.x1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [12138, 10368, 18580, 22752, 5712], 'label': '31104.fx.192.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.d1', 'old_label': '192.g1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.g1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
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id: 186248578
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '192.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.m1', '64.b1', '96.x1'], 'contains': ['384.e1', '576.t1', '576.w1', '576.x1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [12138, 10368, 6484, 22752, 5712], 'label': '31104.fx.192.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.d1', 'old_label': '192.h1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.h1', 'subgroup_fusion': None, 'weyl_group': '324.121'}
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id: 186248579
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '18.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.l1', '9.d1'], 'contains': ['36.n1', '36.o1', '36.w1', '36.bs1', '36.cz1', '54.bp1', '54.br1'], 'core': '72.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [5713, 10368, 72, 2592, 12138, 12096, 22752, 18576, 15552], 'label': '31104.fx.18.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '18.z1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.z1', 'subgroup_fusion': None, 'weyl_group': '576.7160'}
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id: 186248580
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '192.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.y1', '64.c1', '96.q1', '96.v1', '96.bb1'], 'contains': ['384.b1', '576.ba1', '576.bc1', '576.be1', '576.bj1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [2670, 22752, 76, 10368, 12096], 'label': '31104.fx.192.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bd1', 'old_label': '192.i1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.i1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
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id: 186248581
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '192.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.o1', '64.c1', '96.o1', '96.w1', '96.ba1'], 'contains': ['384.d1', '576.y1', '576.z1', '576.ba1', '576.bf1', '576.bg1', '576.bk1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [26047, 10368, 8304, 22752, 3100], 'label': '31104.fx.192.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bc1', 'old_label': '192.j1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.j1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186248582
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '192.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.p1', '64.c1', '96.x1'], 'contains': ['384.e1', '576.ba1', '576.bh1', '576.bi1', '576.bl1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [26047, 10368, 22752, 8304, 4540], 'label': '31104.fx.192.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.x1', 'old_label': '192.k1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.k1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
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id: 186248583
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '192.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.z1', '64.c1', '96.r1', '96.u1', '96.bb1'], 'contains': ['384.b1', '576.bb1', '576.bd1', '576.bj1', '576.bk1', '576.bl1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [6, 10368, 5712, 12096, 22752], 'label': '31104.fx.192.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.d1', 'old_label': '192.l1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.l1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
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id: 186248584
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '192.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.j1', '64.d1', '96.b1', '96.s1', '96.bc1'], 'contains': ['384.a1', '576.bm1', '576.bn1', '576.bp1', '576.bu1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [10405, 12384, 10368, 12940, 1728], 'label': '31104.fx.192.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.a1', 'old_label': '192.m1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.m1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186248585
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '192.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.k1', '48.ba1', '64.d1', '96.t1', '96.u1', '96.v1'], 'contains': ['384.b1', '576.bm1', '576.bo1', '576.bq1', '576.br1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [10405, 10368, 22752, 16080, 1728], 'label': '31104.fx.192.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bd1', 'old_label': '192.n1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.n1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186248586
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '192.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.l1', '48.m1', '64.d1'], 'contains': ['384.c1', '576.bn1', '576.bp1', '576.bq1', '576.bv1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [10405, 12384, 10368, 6484, 9168], 'label': '31104.fx.192.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '192.o1', 'old_label': '192.o1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.o1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 186248587
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '192.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.n1', '64.d1', '96.p1', '96.w1'], 'contains': ['384.d1', '576.bn1', '576.bo1', '576.bs1', '576.bw1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [10405, 16080, 22752, 10368, 30964], 'label': '31104.fx.192.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bc1', 'old_label': '192.p1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.p1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186248588
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '192.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.o1', '64.d1', '96.x1'], 'contains': ['384.e1', '576.bo1', '576.bp1', '576.bq1', '576.bt1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [10405, 22752, 10368, 30964, 9168], 'label': '31104.fx.192.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.x1', 'old_label': '192.q1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.q1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186248589
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '192.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.p1', '96.a1', '96.c1', '96.bc1'], 'contains': ['384.a1', '576.bx1', '576.by1', '576.by2', '576.bz1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [3132, 10368, 10924, 12096, 2016], 'label': '31104.fx.192.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.d1', 'old_label': '192.r1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.r1', 'subgroup_fusion': None, 'weyl_group': '324.124'}
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id: 186248590
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '18.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.i1', '6.j1', '6.k1', '9.c1'], 'contains': ['36.b1', '36.ca1', '36.co1', '54.bj1', '54.bk1', '54.bu1', '72.eu1'], 'core': '36.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [10405, 15552, 10368, 16056, 12138, 16080, 2592, 432, 22752], 'label': '31104.fx.18.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '18.ba1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.ba1', 'subgroup_fusion': None, 'weyl_group': '1152.155790'}
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id: 186248591
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '192.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.r1', '64.e1', '96.d1', '96.s1', '96.bc1'], 'contains': ['384.a1', '576.cd1', '576.ce1', '576.cf1', '576.ci1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [1, 12384, 12096, 10924, 10368], 'label': '31104.fx.192.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.a1', 'old_label': '192.s1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.s1', 'subgroup_fusion': None, 'weyl_group': '324.124'}
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id: 186248592
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '192.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.s1', '48.bb1', '64.e1', '96.t1', '96.y1', '96.bb1'], 'contains': ['384.b1', '576.cb1', '576.cc1', '576.cd1', '576.cj1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [1, 10368, 12096, 5712, 22752], 'label': '31104.fx.192.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bd1', 'old_label': '192.t1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.t1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
-
id: 186248593
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '192.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.t1', '64.e1', '96.p1', '96.z1', '96.ba1'], 'contains': ['384.d1', '576.cg1', '576.ch1', '576.ci1', '576.cj1', '576.ck1', '576.cl1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [1, 10368, 18580, 5712, 22752], 'label': '31104.fx.192.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.d1', 'old_label': '192.u1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.u1', 'subgroup_fusion': None, 'weyl_group': '1944.2342'}
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id: 186248594
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': ['144.fy1'], 'conjugacy_class_count': 2, 'contained_in': ['72.b1', '72.cr1', '72.cu1', '72.cv1', '108.a1', '108.dq1', '108.dy1', '108.ej1', '108.ek1', '108.fb1', '108.fp1'], 'contains': ['648.a1', '648.fy1', '864.da1', '864.gf1'], 'core': '216.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [5712, 15552, 2592, 10368, 15624, 432], 'label': '31104.fx.216.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': ['72.b1', '108.a1'], 'normal_contains': ['648.a1'], 'normalizer': '1.a1', 'old_label': '216.a1', 'projective_image': '31104.fx', 'quotient_action_image': '72.46', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '216.a1', 'subgroup_fusion': None, 'weyl_group': '3456.di'}
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id: 186248595
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['72.a1', '72.b1', '72.cx1', '72.cy1', '72.cz1', '108.dv1', '108.ee1', '108.eo1', '108.ex1', '108.fr1'], 'contains': ['432.en1', '432.hn1', '648.a1', '648.fv1'], 'core': '216.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [16056, 10368, 22752, 18576, 18144, 15552], 'label': '31104.fx.216.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.b1', 'normal_contained_in': ['72.a1', '72.b1'], 'normal_contains': ['648.a1', '3456.a1'], 'normalizer': '1.a1', 'old_label': '216.b1', 'projective_image': '31104.fx', 'quotient_action_image': '72.46', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '216.b1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186248596
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.c1', '108.cr1'], 'contains': ['432.c1', '432.h1', '432.bc1', '432.bj1', '432.bo1', '432.bt1', '432.cu1', '648.b1', '648.c1', '648.d1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1, 10368, 22752, 36, 16056, 15552], 'label': '31104.fx.216.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cr1', 'old_label': '216.c1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.c1', 'subgroup_fusion': None, 'weyl_group': '72.49'}
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id: 186248597
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.c1', '108.cs1'], 'contains': ['432.b1', '432.i1', '432.z1', '432.bk1', '432.bn1', '432.cd1', '432.cr1', '648.b1', '648.e1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [20737, 22752, 1728, 36, 16056, 15552], 'label': '31104.fx.216.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cs1', 'old_label': '216.d1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.d1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186248598
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.c1', '108.cu1'], 'contains': ['432.e1', '432.j1', '432.ba1', '432.bl1', '432.bp1', '432.ce1', '432.cs1', '648.c1', '648.e1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [20737, 12384, 1728, 36, 16056, 15552], 'label': '31104.fx.216.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cu1', 'old_label': '216.e1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.e1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186248599
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.c1', '108.ct1'], 'contains': ['432.f1', '432.k1', '432.bb1', '432.bm1', '432.bq1', '432.cf1', '432.ct1', '648.d1', '648.e1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [20737, 12384, 1728, 36, 2664, 18144], 'label': '31104.fx.216.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ct1', 'old_label': '216.f1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.f1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186248600
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1', '108.cr1'], 'contains': ['432.h1', '432.u1', '432.bc1', '432.br1', '432.bs1', '432.ck1', '432.cq1', '648.f1', '648.g1', '648.h1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1, 10368, 22752, 2628, 16056, 15552], 'label': '31104.fx.216.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cr1', 'old_label': '216.g1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.g1', 'subgroup_fusion': None, 'weyl_group': '72.49'}
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id: 186248601
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '18.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.i1', '9.b1'], 'contains': ['36.bv1', '36.cc1', '36.cr1', '54.bm1', '54.bu1', '72.ev1'], 'core': '108.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [26485, 15552, 22752, 2664, 6, 12096, 2592, 18576, 28012], 'label': '31104.fx.18.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '18.bb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bb1', 'subgroup_fusion': None, 'weyl_group': '3456.gu'}
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id: 186248602
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.d1', '108.cs1'], 'contains': ['432.i1', '432.t1', '432.z1', '432.bx1', '432.ca1', '432.cj1', '432.cn1', '648.f1', '648.i1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [20737, 22752, 1728, 2628, 16056, 15552], 'label': '31104.fx.216.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cs1', 'old_label': '216.h1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.h1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186248603
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1', '108.cu1'], 'contains': ['432.j1', '432.w1', '432.ba1', '432.by1', '432.cb1', '432.cl1', '432.co1', '648.g1', '648.i1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [20737, 12384, 1728, 2628, 16056, 15552], 'label': '31104.fx.216.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cu1', 'old_label': '216.i1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.i1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186248604
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1', '108.ct1'], 'contains': ['432.k1', '432.x1', '432.bb1', '432.bz1', '432.cc1', '432.cm1', '432.cp1', '648.h1', '648.i1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [20737, 12384, 1728, 15588, 2664, 18144], 'label': '31104.fx.216.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ct1', 'old_label': '216.j1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.j1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186248605
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.e1', '108.b1', '108.c1', '108.j1'], 'contains': ['432.cv1', '432.da1', '432.dh1', '432.hx1', '432.ie1', '432.ip1', '432.kk1', '648.j1', '648.k1', '648.l1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26047, 10368, 12096, 36, 18648, 18576], 'label': '31104.fx.216.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.k1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.k1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186248606
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.e1', '108.b1', '108.c1', '108.l1'], 'contains': ['432.cv1', '432.db1', '432.de1', '432.hy1', '432.if1', '432.jd1', '432.jv1', '648.k1', '648.m1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26047, 22752, 12096, 36, 18648, 18576], 'label': '31104.fx.216.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.l1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.l1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186248607
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.e1', '108.k1'], 'contains': ['432.cw1', '432.dc1', '432.df1', '432.hz1', '432.ig1', '432.je1', '432.jw1', '648.l1', '648.m1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [26047, 22752, 12096, 36, 15552, 2592], 'label': '31104.fx.216.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.k1', 'old_label': '216.m1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.m1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186248608
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cr1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.e1', '108.d1', '108.e1', '108.m1'], 'contains': ['432.cx1', '432.dd1', '432.dg1', '432.ia1', '432.ii1', '432.jf1', '432.jx1', '648.j1', '648.m1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [19135, 10368, 22752, 36, 18648, 18576], 'label': '31104.fx.216.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.n1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.n1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186248609
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.f1', '108.d1', '108.n1', '108.cr1'], 'contains': ['432.bj1', '432.br1', '432.cx1', '432.di1', '432.dx1', '432.ib1', '432.kr1', '648.n1', '648.o1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [1, 10368, 22752, 36, 18144, 2592], 'label': '31104.fx.216.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '216.o1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.o1', 'subgroup_fusion': None, 'weyl_group': '144.154'}
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id: 186248610
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.f1', '108.b1', '108.o1', '108.cs1'], 'contains': ['432.bk1', '432.bx1', '432.cv1', '432.dj1', '432.dv1', '432.ic1', '432.ku1', '648.n1', '648.p1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [20737, 22752, 1728, 36, 18144, 2592], 'label': '31104.fx.216.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '216.p1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.p1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
-
id: 186248611
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.f1', '108.p1', '108.ct1', '108.cu1'], 'contains': ['432.bl1', '432.bm1', '432.by1', '432.bz1', '432.cy1', '432.dk1', '432.dw1', '432.id1', '432.kv1', '648.o1', '648.p1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [20737, 12384, 1728, 36, 18144, 15552], 'label': '31104.fx.216.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '216.q1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.q1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186248612
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '4.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': ['7776.bd1', '7776.ba1', '7776.bc1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '2.b1'], 'contains': ['8.a1', '12.a1', '12.j1', '12.k1', '16.a1'], 'core': '4.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [36, 12384, 18576, 18144, 10368, 76, 16056, 12096, 15552, 5712], 'label': '31104.fx.4.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': ['2.a1', '2.b1'], 'normal_contains': ['8.a1', '12.a1'], 'normalizer': '1.a1', 'old_label': '4.a1', 'projective_image': '31104.fx', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.a1', 'subgroup_fusion': None, 'weyl_group': '31104.fx'}
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id: 186248613
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '18.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.j1', '9.a1'], 'contains': ['36.bw1', '36.cg1', '36.cs1', '54.bl1', '54.bn1', '54.bu1', '288.dr1'], 'core': '108.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [12133, 15552, 22752, 16056, 6, 5712, 18144, 18576, 20812], 'label': '31104.fx.18.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '18.bc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bc1', 'subgroup_fusion': None, 'weyl_group': '3456.di'}
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id: 186248614
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.g1', '108.c1', '108.o1', '108.cv1'], 'contains': ['432.cv1', '432.dy1', '432.ea1', '432.ih1', '432.la1', '648.q1', '648.v1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [21169, 22752, 1728, 36, 18144, 2592], 'label': '31104.fx.216.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '216.r1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.r1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
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id: 186248615
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.h1', '108.t1', '108.cs1', '108.cv1'], 'contains': ['432.bn1', '432.cj1', '432.cv1', '432.dz1', '432.eb1', '648.r1', '648.w1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5689, 22752, 1728, 36, 2592, 15552], 'label': '31104.fx.216.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.be1', 'old_label': '216.s1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.s1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186248616
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.g1', '108.e1', '108.n1', '108.cw1'], 'contains': ['432.cx1', '432.ec1', '432.ee1', '432.ij1', '432.lb1', '648.q1', '648.s1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [433, 10368, 22752, 36, 18144, 2592], 'label': '31104.fx.216.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '216.t1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.t1', 'subgroup_fusion': None, 'weyl_group': '144.154'}
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id: 186248617
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.h1', '108.v1', '108.cr1', '108.cw1'], 'contains': ['432.bo1', '432.ck1', '432.cx1', '432.ed1', '432.ef1', '648.r1', '648.t1', '648.u1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [16057, 10368, 22752, 36, 2592, 15552], 'label': '31104.fx.216.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bd1', 'old_label': '216.u1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.u1', 'subgroup_fusion': None, 'weyl_group': '72.49'}
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id: 186248618
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.g1', '108.p1', '108.cx1', '108.cy1'], 'contains': ['432.cy1', '432.eg1', '432.ej1', '432.ik1', '432.lc1', '648.s1', '648.v1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [8209, 12384, 1728, 36, 15552, 2592], 'label': '31104.fx.216.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '216.v1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.v1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186248619
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.h1', '108.w1', '108.cu1', '108.cx1'], 'contains': ['432.bp1', '432.cl1', '432.cy1', '432.eh1', '432.ek1', '648.t1', '648.w1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [5689, 12384, 1728, 36, 18144, 15552], 'label': '31104.fx.216.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '216.w1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.w1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186248620
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.h1', '108.w1', '108.ct1', '108.cy1'], 'contains': ['432.bq1', '432.cm1', '432.cy1', '432.ei1', '432.ek2', '648.u1', '648.w1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [23401, 12384, 1728, 36, 15552, 18144], 'label': '31104.fx.216.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '216.x1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.x1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186248621
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.i1', '108.b1', '108.f1', '108.x1'], 'contains': ['432.da1', '432.de1', '432.dj1', '432.il1', '432.io1', '432.ju1', '432.ky1', '648.x1', '648.z1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26485, 12096, 18576, 12138, 18648, 22752], 'label': '31104.fx.216.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.y1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.y1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
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id: 186248622
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.k1', '108.c1', '108.g1', '108.x1'], 'contains': ['432.da1', '432.de1', '432.dy1', '432.im1', '432.it1', '432.kd1', '432.lo1', '648.y1', '648.bd1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [29077, 12096, 18576, 12138, 18648, 22752], 'label': '31104.fx.216.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.z1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.z1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
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id: 186248623
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.j1', '108.f1', '108.g1', '108.j1'], 'contains': ['432.da1', '432.dh1', '432.dq1', '432.in1', '432.iq1', '432.kl1', '432.lg1', '648.ba1', '648.bb1', '648.bc1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26047, 10368, 12096, 2628, 18648, 18576], 'label': '31104.fx.216.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.ba1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ba1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186248624
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '18.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10368.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.k1'], 'contains': ['36.bx1', '36.ch1', '36.ct1', '54.bo1', '54.bu1', '288.ds1'], 'core': '108.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [10405, 15552, 10368, 16056, 12138, 16080, 18144, 18576, 24268], 'label': '31104.fx.18.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1', 'old_label': '18.bd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bd1', 'subgroup_fusion': None, 'weyl_group': '1728.46101'}
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id: 186248625
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.dg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.i1', '108.d1', '108.h1', '108.bb1'], 'contains': ['432.dd1', '432.dg1', '432.di1', '432.iu1', '432.jb1', '432.jt1', '432.kt1', '648.x1', '648.bh1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26485, 10368, 18576, 12138, 18648, 22752], 'label': '31104.fx.216.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.bb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bb1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186248626
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.j1', '108.f1', '108.g1', '108.l1'], 'contains': ['432.db1', '432.de1', '432.dq1', '432.iv1', '432.jg1', '432.jy1', '432.lh1', '648.bb1', '648.bg1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26047, 22752, 12096, 2628, 18648, 18576], 'label': '31104.fx.216.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.bc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bc1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186248627
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.j1', '108.k1'], 'contains': ['432.dc1', '432.df1', '432.dr1', '432.iw1', '432.jh1', '432.jz1', '432.li1', '648.bc1', '648.bg1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [26047, 22752, 12096, 18612, 15552, 2592], 'label': '31104.fx.216.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.k1', 'old_label': '216.bd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bd1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186248628
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.j1', '108.h1', '108.i1', '108.m1'], 'contains': ['432.dd1', '432.dg1', '432.ds1', '432.ix1', '432.ji1', '432.ka1', '432.lj1', '648.ba1', '648.bg1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [19135, 10368, 22752, 2628, 18648, 18576], 'label': '31104.fx.216.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.be1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.be1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186248629
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ed1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.k1', '108.e1', '108.i1', '108.bb1'], 'contains': ['432.dd1', '432.dg1', '432.ec1', '432.iy1', '432.jo1', '432.kf1', '432.ls1', '648.y1', '648.bi1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [29077, 10368, 18576, 12138, 18648, 22752], 'label': '31104.fx.216.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.bf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bf1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186248630
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.i1', '108.b1', '108.f1', '108.bc1'], 'contains': ['432.db1', '432.dh1', '432.dj1', '432.iz1', '432.jc1', '432.kj1', '432.kz1', '648.z1', '648.bh1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [26485, 10368, 12096, 12138, 18648, 18576], 'label': '31104.fx.216.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '216.bg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bg1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186248631
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.k1', '108.c1', '108.g1', '108.bc1'], 'contains': ['432.db1', '432.dh1', '432.dy1', '432.ja1', '432.jm1', '432.kn1', '432.lp1', '648.bd1', '648.bi1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [29077, 10368, 12096, 12138, 18648, 18576], 'label': '31104.fx.216.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '216.bh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bh1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186248632
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.l1', '108.b1', '108.g1', '108.bk1'], 'contains': ['432.da1', '432.db1', '432.dv1', '432.ir1', '432.jj1', '432.jp1', '432.lk1', '648.be1', '648.bj1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 10368, 18576, 12138, 18648, 12096], 'label': '31104.fx.216.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.bi1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bi1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
-
id: 186248633
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.m1', '108.c1', '108.f1', '108.bk1'], 'contains': ['432.da1', '432.db1', '432.ea1', '432.is1', '432.jl1', '432.jq1', '432.lq1', '648.bf1', '648.bk1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [8305, 10368, 18576, 12138, 18648, 12096], 'label': '31104.fx.216.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.bj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bj1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
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id: 186248634
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.di1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.l1', '108.d1', '108.i1', '108.bl1'], 'contains': ['432.dd1', '432.dx1', '432.jk1', '432.jr1', '432.lm1', '648.bj1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [5713, 10368, 22752, 12138, 18648, 18576], 'label': '31104.fx.216.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '216.bk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bk1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186248635
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '18.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.l1', '9.b1'], 'contains': ['36.bq1', '36.bv1', '36.cx1', '54.bp1', '54.bv1', '72.ex1'], 'core': '108.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1, 15552, 10368, 16056, 12138, 5712, 2592, 432, 12096], 'label': '31104.fx.18.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.be1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.be1', 'subgroup_fusion': None, 'weyl_group': '3456.gu'}
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id: 186248636
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.el1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.m1', '108.e1', '108.h1', '108.bl1'], 'contains': ['432.dd1', '432.ee1', '432.jn1', '432.js1', '432.lt1', '648.bk1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [8305, 10368, 22752, 12138, 18648, 18576], 'label': '31104.fx.216.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '216.bl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bl1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186248637
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.n1', '108.d1', '108.i1', '108.bt1'], 'contains': ['432.dg1', '432.dx1', '432.kc1', '432.kh1', '432.ln1', '648.bl1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [5713, 10368, 22752, 6, 18648, 18576], 'label': '31104.fx.216.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.bm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bm1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186248638
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.o1', '108.e1', '108.h1', '108.bt1'], 'contains': ['432.dg1', '432.ee1', '432.kg1', '432.ki1', '432.lu1', '648.bm1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [8305, 10368, 22752, 6, 18648, 18576], 'label': '31104.fx.216.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.bn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bn1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186248639
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.n1', '108.b1', '108.g1', '108.bx1'], 'contains': ['432.de1', '432.dh1', '432.dv1', '432.kb1', '432.km1', '432.kp1', '432.ll1', '648.bl1', '648.bn1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5713, 10368, 12096, 6, 18648, 18576], 'label': '31104.fx.216.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.bo1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bo1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186248660
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.t1', '108.cf1', '108.cx1', '108.df1'], 'contains': ['432.do1', '432.eh1', '432.ej1', '648.cc1', '648.cf1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [8209, 12384, 1728, 2700, 2592, 15552], 'label': '31104.fx.216.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '216.cf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cf1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186248640
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.o1', '108.c1', '108.f1', '108.bx1'], 'contains': ['432.de1', '432.dh1', '432.ea1', '432.ke1', '432.ko1', '432.kq1', '432.lr1', '648.bm1', '648.bo1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [8305, 10368, 12096, 6, 18648, 18576], 'label': '31104.fx.216.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.bp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bp1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 186248641
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.p1', '108.by1', '108.cr1', '108.cz1'], 'contains': ['432.bs1', '432.bt1', '432.di1', '432.dn1', '432.ef1', '648.bp1', '648.bq1', '648.bq2'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [16057, 10368, 22752, 16092, 2592, 15552], 'label': '31104.fx.216.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bd1', 'old_label': '216.bq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bq1', 'subgroup_fusion': None, 'weyl_group': '144.196'}
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id: 186248642
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.q1', '108.h1', '108.n1', '108.cz1'], 'contains': ['432.di1', '432.ds1', '432.ee1', '432.ks1', '648.br1', '648.bs1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [433, 10368, 22752, 468, 18144, 2592], 'label': '31104.fx.216.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '216.br1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.br1', 'subgroup_fusion': None, 'weyl_group': '288.977'}
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id: 186248643
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.p1', '108.ca1', '108.cs1', '108.dd1'], 'contains': ['432.ca1', '432.cd1', '432.dj1', '432.dl1', '432.eb1', '648.bp1', '648.bt1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5689, 22752, 1728, 16092, 2592, 15552], 'label': '31104.fx.216.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.be1', 'old_label': '216.bs1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bs1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186248644
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.p1', '108.cb1', '108.ct1', '108.df1'], 'contains': ['432.cc1', '432.cf1', '432.dk1', '432.do1', '432.ek2', '648.bq1', '648.bt1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [23401, 12384, 1728, 2700, 15552, 18144], 'label': '31104.fx.216.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '216.bt1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bt1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186248645
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.bt2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.p1', '108.cb1', '108.cu1', '108.de1'], 'contains': ['432.cb1', '432.ce1', '432.dk1', '432.do2', '432.ek1', '648.bq2', '648.bt1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [5689, 12384, 1728, 16092, 18144, 15552], 'label': '31104.fx.216.bt2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '216.bt2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bt2', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186248646
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '18.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.b1', '9.a1'], 'contains': ['36.br1', '36.bw1', '36.dd1', '54.bq1', '54.bs1', '54.bt1', '54.bv1', '288.du1'], 'core': '108.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1, 15552, 22752, 16056, 12138, 5712, 18144, 18576, 20812], 'label': '31104.fx.18.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.bf1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bf1', 'subgroup_fusion': None, 'weyl_group': '3456.di'}
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id: 186248647
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.q1', '108.f1', '108.o1', '108.dd1'], 'contains': ['432.dj1', '432.dq1', '432.ea1', '432.kw1', '432.kw2', '648.br1', '648.bu1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [433, 10368, 1728, 468, 18144, 2592], 'label': '31104.fx.216.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '216.bu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bu1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
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id: 186248648
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.q1', '108.p1', '108.de1', '108.df1'], 'contains': ['432.dk1', '432.dt1', '432.ej1', '432.kx1', '648.bs1', '648.bu1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [8209, 12384, 1728, 18612, 15552, 2592], 'label': '31104.fx.216.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '216.bv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bv1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186248649
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.r1', '108.ce1', '108.cs1', '108.dj1'], 'contains': ['432.cn1', '432.cr1', '432.dl1', '432.dv1', '432.dz1', '648.bv1', '648.bw1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [20737, 22752, 1728, 16092, 2592, 15552], 'label': '31104.fx.216.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.be1', 'old_label': '216.bw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bw1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186248650
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.r1', '108.cf1', '108.cu1', '108.dk1'], 'contains': ['432.co1', '432.cs1', '432.do2', '432.dw1', '432.eh1', '648.bv1', '648.bx1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [20737, 12384, 1728, 16092, 18144, 15552], 'label': '31104.fx.216.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '216.bx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bx1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186248651
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.r1', '108.cf1', '108.ct1', '108.dl1'], 'contains': ['432.cp1', '432.ct1', '432.do1', '432.dw1', '432.ei1', '648.bv1', '648.by1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [20737, 12384, 1728, 2700, 15552, 18144], 'label': '31104.fx.216.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '216.by1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.by1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 186248652
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.r1', '108.cg1', '108.cr1', '108.dm1'], 'contains': ['432.cq1', '432.cu1', '432.dn1', '432.dx1', '432.ed1', '648.bw1', '648.bx1', '648.by1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1, 10368, 22752, 16092, 2592, 15552], 'label': '31104.fx.216.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bd1', 'old_label': '216.bz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bz1', 'subgroup_fusion': None, 'weyl_group': '144.196'}
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id: 186248653
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.s1', '108.ca1', '108.cv1', '108.dj1'], 'contains': ['432.dl1', '432.dy1', '432.eb1', '648.bz1', '648.ce1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5257, 22752, 1728, 16092, 18144, 2592], 'label': '31104.fx.216.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.be1', 'old_label': '216.ca1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ca1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186248654
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.t1', '108.ce1', '108.cv1', '108.dd1'], 'contains': ['432.dl1', '432.dz1', '432.ea1', '648.ca1', '648.cf1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [21169, 22752, 1728, 16092, 15552, 2592], 'label': '31104.fx.216.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.be1', 'old_label': '216.cb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cb1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186248655
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.s1', '108.by1', '108.cw1', '108.dm1'], 'contains': ['432.dn1', '432.ec1', '432.ef1', '648.bz1', '648.cb1', '648.cb2'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [15625, 10368, 22752, 16092, 18144, 2592], 'label': '31104.fx.216.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bd1', 'old_label': '216.cc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cc1', 'subgroup_fusion': None, 'weyl_group': '144.196'}
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id: 186248656
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.t1', '108.cg1', '108.cw1', '108.cz1'], 'contains': ['432.dn1', '432.ed1', '432.ee1', '648.ca1', '648.cc1', '648.cd1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [433, 10368, 22752, 16092, 15552, 2592], 'label': '31104.fx.216.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bd1', 'old_label': '216.cd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cd1', 'subgroup_fusion': None, 'weyl_group': '144.196'}
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id: 186248657
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '18.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.b1', '6.l1', '9.c1'], 'contains': ['36.b1', '36.bt1', '36.df1', '54.bq1', '54.br1', '54.bv1', '72.ey1'], 'core': '36.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1, 15552, 10368, 16056, 12138, 22752, 2592, 432, 5712], 'label': '31104.fx.18.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '18.bg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bg1', 'subgroup_fusion': None, 'weyl_group': '10368.je'}
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id: 186248658
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.s1', '108.cb1', '108.cx1', '108.dl1'], 'contains': ['432.do1', '432.eg1', '432.ek1', '648.cb1', '648.ce1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [5689, 12384, 1728, 2700, 18144, 15552], 'label': '31104.fx.216.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '216.ce1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ce1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186248659
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ce2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.s1', '108.cb1', '108.cy1', '108.dk1'], 'contains': ['432.do2', '432.eg1', '432.ek2', '648.cb2', '648.ce1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [23401, 12384, 1728, 16092, 18144, 15552], 'label': '31104.fx.216.ce2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '216.ce2', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ce2', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186248661
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.t1', '108.cf1', '108.cy1', '108.de1'], 'contains': ['432.do2', '432.ei1', '432.ej1', '648.cd1', '648.cf1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [8209, 12384, 1728, 16092, 2592, 15552], 'label': '31104.fx.216.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '216.cg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cg1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186248662
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.u1', '108.g1', '108.o1', '108.dj1'], 'contains': ['432.dq1', '432.dv1', '432.dy1', '432.ld1', '432.ld2', '648.cg1', '648.ch1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [20737, 22752, 1728, 468, 18144, 2592], 'label': '31104.fx.216.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '216.ch1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ch1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
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id: 186248663
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.u1', '108.p1', '108.dk1', '108.dl1'], 'contains': ['432.dt1', '432.dw1', '432.eg1', '432.le1', '648.cg1', '648.ci1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [20737, 12384, 1728, 18612, 15552, 2592], 'label': '31104.fx.216.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '216.ci1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ci1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186248664
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.u1', '108.i1', '108.n1', '108.dm1'], 'contains': ['432.ds1', '432.dx1', '432.ec1', '432.lf1', '648.ch1', '648.ci1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [1, 10368, 22752, 468, 18144, 2592], 'label': '31104.fx.216.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '216.cj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cj1', 'subgroup_fusion': None, 'weyl_group': '288.977'}
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id: 186248665
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.v1', '108.t1', '108.dd1', '108.dj1'], 'contains': ['432.dq1', '432.dz1', '432.eb1', '648.cj1', '648.cm1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [5689, 22752, 1728, 468, 15552, 2592], 'label': '31104.fx.216.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.be1', 'old_label': '216.ck1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ck1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186248666
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.v1', '108.v1', '108.cz1', '108.dm1'], 'contains': ['432.ds1', '432.ed1', '432.ef1', '648.cj1', '648.ck1', '648.cl1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [16057, 10368, 22752, 468, 15552, 2592], 'label': '31104.fx.216.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bd1', 'old_label': '216.cl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cl1', 'subgroup_fusion': None, 'weyl_group': '144.196'}
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id: 186248667
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.v1', '108.w1', '108.df1', '108.dk1'], 'contains': ['432.dt1', '432.eh1', '432.ek2', '648.ck1', '648.cm1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [23401, 12384, 1728, 18612, 18144, 15552], 'label': '31104.fx.216.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '216.cm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cm1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186248668
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '18.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.m1'], 'contains': ['36.by1', '36.cf1', '36.dc1', '54.bx1', '54.ca1', '54.cb1', '54.cc1', '54.cd1', '288.dw1'], 'core': '648.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1, 15552, 10368, 16056, 22758, 28464, 18144, 18576, 76], 'label': '31104.fx.18.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bh1', 'old_label': '18.bh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bh1', 'subgroup_fusion': None, 'weyl_group': '1728.47856'}
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id: 186248669
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.v1', '108.w1', '108.de1', '108.dl1'], 'contains': ['432.dt1', '432.ei1', '432.ek1', '648.cl1', '648.cm1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [5689, 12384, 1728, 18612, 2592, 15552], 'label': '31104.fx.216.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '216.cn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cn1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 186248670
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.w1', '108.k1', '108.r1', '108.du1'], 'contains': ['432.a1', '432.b1', '432.l1', '432.m1', '432.cw1', '432.dr1', '432.el1', '432.ly1', '432.ma1', '432.no1', '432.nq1', '648.cn1', '648.cq1', '648.cr1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [36, 10368, 12096, 18144, 16056, 18576], 'label': '31104.fx.216.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bb1', 'old_label': '216.co1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.co1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186248671
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.w1', '108.j1', '108.l1', '108.o1', '108.q1', '108.s1', '108.t1', '108.du1'], 'contains': ['432.a1', '432.l2', '432.cv1', '432.dq1', '432.em1', '432.ly1', '432.lz1', '432.no2', '432.np1', '648.cn1', '648.cp1', '648.cq1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [36, 10368, 12096, 16056, 2592, 18576], 'label': '31104.fx.216.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '216.cp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cp1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186248672
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.w1', '108.m1', '108.n1', '108.u1', '108.v1', '108.dv1'], 'contains': ['432.c1', '432.n1', '432.cx1', '432.ds1', '432.en1', '432.mb1', '432.nr1', '648.cn1', '648.co1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [36, 10368, 22752, 18576, 18144, 16056], 'label': '31104.fx.216.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '216.cq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cq1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 186248673
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.w1', '108.p1', '108.w1', '108.dw1'], 'contains': ['432.e1', '432.g1', '432.p1', '432.r1', '432.cy1', '432.dt1', '432.eo1', '432.mc1', '432.ns1', '648.co1', '648.cp1', '648.cr1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [36, 12384, 12096, 2592, 18576, 72], 'label': '31104.fx.216.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '216.cr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cr1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186248674
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.w1', '108.dw1'], 'contains': ['432.d1', '432.f1', '432.g1', '432.o1', '432.q1', '432.r2', '432.cz1', '432.du1', '432.ep1', '432.mc1', '432.ns2', '648.co1', '648.cq1', '648.cr1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [36, 12384, 12096, 16056, 18576, 18144], 'label': '31104.fx.216.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.dw1', 'old_label': '216.cs1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cs1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 186248675
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.gc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.x1', '108.j1', '108.x1', '108.y1', '108.z1', '108.ba1', '108.bk1', '108.dx1'], 'contains': ['432.da1', '432.em1', '432.md1', '432.me1', '432.ob1', '648.cs1', '648.ct1', '648.cu1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [17371, 18576, 10368, 16056, 2592, 12096], 'label': '31104.fx.216.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '216.ct1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ct1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
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id: 186248676
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.gc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.x1', '108.k1', '108.bd1', '108.ea1'], 'contains': ['432.dc1', '432.el1', '432.mi1', '432.ml1', '432.od1', '648.cu1', '648.cv1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [17371, 22752, 2592, 15552, 18576, 12096], 'label': '31104.fx.216.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.s1', 'old_label': '216.cu1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cu1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186248677
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.gc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.x1', '108.l1', '108.bc1', '108.be1', '108.bg1', '108.bh1', '108.bk1', '108.ea1'], 'contains': ['432.db1', '432.em1', '432.mh1', '432.ml1', '432.oc1', '648.ct1', '648.cv1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [17371, 22752, 18576, 16056, 2592, 12096], 'label': '31104.fx.216.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '216.cv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cv1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186248678
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.gc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.x1', '108.m1', '108.bb1', '108.bf1', '108.bi1', '108.bj1', '108.bl1', '108.ee1'], 'contains': ['432.dd1', '432.en1', '432.mk1', '432.mo1', '432.og1', '648.cs1', '648.cv1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [17371, 22752, 18576, 16056, 2592, 10368], 'label': '31104.fx.216.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '216.cw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cw1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186248679
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '18.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.m1', '9.a1'], 'contains': ['36.bz1', '36.cg1', '36.dd1', '54.bw1', '54.bz1', '54.cb1', '54.cd1', '288.dx1'], 'core': '216.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1, 15552, 10368, 16056, 6, 5712, 18144, 18576, 76], 'label': '31104.fx.18.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.bi1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bi1', 'subgroup_fusion': None, 'weyl_group': '3456.di'}
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id: 186248680
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ep1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.y1', '108.k1', '108.bm1', '108.ei1'], 'contains': ['432.df1', '432.el1', '432.ms1', '432.mx1', '432.oe1', '648.cw1', '648.cz1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [26047, 12096, 2592, 15552, 18576, 22752], 'label': '31104.fx.216.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bb1', 'old_label': '216.cx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cx1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186248681
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ep1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.y1', '108.l1', '108.x1', '108.bn1', '108.bp1', '108.bq1', '108.bx1', '108.ei1'], 'contains': ['432.de1', '432.em1', '432.mr1', '432.mx1', '432.oe2', '648.cw1', '648.cy1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [26047, 12096, 18576, 16056, 2592, 22752], 'label': '31104.fx.216.cy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '216.cy1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cy1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186248682
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ep1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.y1', '108.m1', '108.bb1', '108.bo1', '108.br1', '108.bs1', '108.bt1', '108.eo1'], 'contains': ['432.dg1', '432.en1', '432.mw1', '432.na1', '432.oh1', '648.cw1', '648.cx1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [26047, 10368, 18576, 16056, 2592, 22752], 'label': '31104.fx.216.cz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '216.cz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cz1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186248683
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ep1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.y1', '108.j1', '108.bc1', '108.bu1', '108.bv1', '108.bw1', '108.bx1', '108.eu1'], 'contains': ['432.dh1', '432.em1', '432.nb1', '432.ne1', '432.of1', '648.cx1', '648.cy1', '648.cz1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [6, 22752, 12096, 18576, 18144, 16056], 'label': '31104.fx.216.da1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '216.da1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.da1', 'subgroup_fusion': None, 'weyl_group': '288.977'}
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id: 186248684
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.z1', '108.n1', '108.bb1', '108.by1', '108.bz1', '108.ex1'], 'contains': ['432.di1', '432.ec1', '432.en1', '432.nf1', '648.da1', '648.db1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [10405, 2592, 10368, 18576, 18144, 22752], 'label': '31104.fx.216.db1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '216.db1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.db1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
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id: 186248685
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.z1', '108.o1', '108.x1', '108.bc1', '108.ca1', '108.cc1', '108.cd1', '108.ey1'], 'contains': ['432.dj1', '432.dy1', '432.em1', '432.ng1', '432.nh1', '648.da1', '648.dc1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [10405, 1728, 2592, 18576, 18144, 22752], 'label': '31104.fx.216.dc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '216.dc1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dc1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186248686
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.z1', '108.p1', '108.cb1', '108.fe1'], 'contains': ['432.dk1', '432.eg1', '432.eo1', '432.nl1', '648.db1', '648.dc1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [10405, 1728, 2592, 18576, 15552, 12384], 'label': '31104.fx.216.dd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '216.dd1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dd1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186248687
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ba1', '108.bd1', '108.bm1', '108.du1'], 'contains': ['432.l2', '432.m1', '432.s1', '432.t1', '432.dm1', '432.el1', '432.no1', '432.no2', '432.nq1', '648.dd1', '648.dg1', '648.dh1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [15588, 10368, 12096, 18144, 16056, 18576], 'label': '31104.fx.216.de1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bb1', 'old_label': '216.de1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.de1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 186248688
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ba1', '108.y1', '108.be1', '108.bn1', '108.bu1', '108.ca1', '108.ce1', '108.du1'], 'contains': ['432.l1', '432.s1', '432.dl1', '432.em1', '432.no1', '432.np1', '648.dd1', '648.df1', '648.dg1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [15588, 10368, 12096, 16056, 2592, 18576], 'label': '31104.fx.216.df1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '216.df1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.df1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186248689
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ba1', '108.bf1', '108.bo1', '108.by1', '108.cg1', '108.dv1'], 'contains': ['432.n1', '432.u1', '432.dn1', '432.en1', '432.nr1', '648.dd1', '648.de1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [15588, 10368, 22752, 18576, 18144, 16056], 'label': '31104.fx.216.dg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '216.dg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dg1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186248690
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '18.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.m1', '6.n1', '9.c1'], 'contains': ['36.ca1', '36.ck1', '36.df1', '54.bw1', '54.bx1', '54.by1', '54.cd1', '72.fb1'], 'core': '72.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1, 15552, 10368, 16056, 6, 22752, 2592, 432, 5712], 'label': '31104.fx.18.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '18.bj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bj1', 'subgroup_fusion': None, 'weyl_group': '3456.de'}
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id: 186248691
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ba1', '108.cb1', '108.cf1', '108.dw1'], 'contains': ['432.p1', '432.r2', '432.w1', '432.y1', '432.do1', '432.do2', '432.eo1', '432.ns2', '648.de1', '648.df1', '648.dh1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [18180, 12384, 12096, 2592, 18576, 72], 'label': '31104.fx.216.dh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '216.dh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dh1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 186248692
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ba1', '108.dw1'], 'contains': ['432.o1', '432.q1', '432.r1', '432.v1', '432.x1', '432.y1', '432.dp1', '432.dp2', '432.ep1', '432.ns1', '432.ns2', '648.de1', '648.dg1', '648.dh1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [18252, 12384, 12096, 16056, 18576, 18144], 'label': '31104.fx.216.di1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.dw1', 'old_label': '216.di1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.di1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 186248693
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.bb1', '108.o1', '108.bk1', '108.bx1', '108.ce1', '108.ch1', '108.ci1', '108.fl1'], 'contains': ['432.dv1', '432.ea1', '432.em1', '432.nt1', '432.nu1', '648.di1', '648.dj1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1, 10368, 2592, 18576, 18144, 1728], 'label': '31104.fx.216.dj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '216.dj1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dj1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186248694
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bb1', '108.p1', '108.cf1', '108.fm1'], 'contains': ['432.dw1', '432.ej1', '432.eo1', '432.nv1', '648.di1', '648.dk1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1, 12384, 2592, 18576, 15552, 1728], 'label': '31104.fx.216.dk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '216.dk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dk1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186248695
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bb1', '108.n1', '108.bl1', '108.bt1', '108.cg1', '108.cj1', '108.ck1', '108.fr1'], 'contains': ['432.dx1', '432.ee1', '432.en1', '432.nz1', '648.dj1', '648.dk1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1, 10368, 22752, 18576, 18144, 2592], 'label': '31104.fx.216.dl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '216.dl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dl1', 'subgroup_fusion': None, 'weyl_group': '288.977'}
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id: 186248696
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.gc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.bc1', '108.q1', '108.bh1', '108.bp1', '108.bu1', '108.cc1', '108.ch1', '108.dx1'], 'contains': ['432.em1', '432.ob1', '648.dl1', '648.dt1', '648.du1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1819, 18576, 2592, 16056, 12096, 10368], 'label': '31104.fx.216.dm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '216.dm1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dm1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
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id: 186248697
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.gc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.bc1', '108.r1', '108.bm1', '108.ea1'], 'contains': ['432.el1', '432.oc1', '432.od1', '648.dm1', '648.du1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [17299, 22752, 18576, 15552, 12096, 2592], 'label': '31104.fx.216.dn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.s1', 'old_label': '216.dn1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dn1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186248698
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.gc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.bc1', '108.s1', '108.ba1', '108.bn1', '108.bv1', '108.cd1', '108.ch1', '108.ea1'], 'contains': ['432.em1', '432.od1', '648.dm1', '648.dt1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [27690, 10368, 18576, 2592, 12096, 2664], 'label': '31104.fx.216.do1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '216.do1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.do1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186248699
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.bd1', '108.t1', '108.z1', '108.bg1', '108.bp1', '108.bv1', '108.ce1', '108.ey1'], 'contains': ['432.dz1', '432.em1', '648.dn1', '648.dv1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [26461, 1728, 2592, 18576, 22752, 15552], 'label': '31104.fx.216.dp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '216.dp1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dp1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186248700
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ep1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.be1', '108.r1', '108.bd1', '108.ei1'], 'contains': ['432.el1', '432.oe1', '432.oe2', '648.do1', '648.dx1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [25975, 12096, 18576, 15552, 22752, 2592], 'label': '31104.fx.216.dq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bb1', 'old_label': '216.dq1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dq1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186248701
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '18.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.n1', '9.b1'], 'contains': ['36.cb1', '36.cc1', '36.cx1', '54.bw1', '54.ce1', '72.fd1'], 'core': '216.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [5713, 15552, 22752, 2664, 6, 12096, 2592, 18576, 5260], 'label': '31104.fx.18.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.bk1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bk1', 'subgroup_fusion': None, 'weyl_group': '3456.gu'}
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id: 186248702
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ep1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.be1', '108.s1', '108.z1', '108.be1', '108.bw1', '108.cc1', '108.ci1', '108.ei1'], 'contains': ['432.em1', '432.oe1', '648.do1', '648.dw1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [10495, 12096, 18576, 16056, 22752, 2592], 'label': '31104.fx.216.dr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '216.dr1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dr1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186248703
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ep1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.be1', '108.q1', '108.y1', '108.bg1', '108.bq1', '108.cd1', '108.ci1', '108.eu1'], 'contains': ['432.em1', '432.of1', '648.dp1', '648.dw1', '648.dx1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [10495, 10368, 12096, 16056, 2592, 18576], 'label': '31104.fx.216.ds1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '216.ds1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ds1', 'subgroup_fusion': None, 'weyl_group': '288.977'}
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id: 186248704
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.bf1', '108.t1', '108.ba1', '108.bh1', '108.bq1', '108.bw1', '108.ca1', '108.fl1'], 'contains': ['432.eb1', '432.em1', '648.dq1', '648.dy1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [16057, 10368, 2592, 18576, 1728, 15552], 'label': '31104.fx.216.dt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '216.dt1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dt1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186248705
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.gc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.bc1', '108.u1', '108.bj1', '108.bo1', '108.br1', '108.bz1', '108.cj1', '108.ee1'], 'contains': ['432.en1', '432.og1', '648.dl1', '648.dm1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1819, 22752, 18576, 16056, 10368, 2592], 'label': '31104.fx.216.du1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '216.du1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.du1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186248706
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.dv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bd1', '108.v1', '108.bi1', '108.br1', '108.cg1', '108.ex1'], 'contains': ['432.ed1', '432.en1', '648.dn1', '648.dr1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [26461, 2592, 15552, 18576, 22752, 10368], 'label': '31104.fx.216.dv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '216.dv1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dv1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
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id: 186248707
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ep1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.be1', '108.u1', '108.bf1', '108.bi1', '108.bs1', '108.bz1', '108.ck1', '108.eo1'], 'contains': ['432.en1', '432.oh1', '648.do1', '648.dp1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [10495, 10368, 18576, 16056, 22752, 2592], 'label': '31104.fx.216.dw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '216.dw1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dw1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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id: 186248708
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.dx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bf1', '108.v1', '108.bj1', '108.bs1', '108.by1', '108.fr1'], 'contains': ['432.ef1', '432.en1', '648.dq1', '648.ds1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [16057, 10368, 22752, 18576, 15552, 2592], 'label': '31104.fx.216.dx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '216.dx1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dx1', 'subgroup_fusion': None, 'weyl_group': '288.977'}
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id: 186248709
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.ct1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bd1', '108.w1', '108.cf1', '108.fe1'], 'contains': ['432.eh1', '432.ei1', '432.eo1', '648.dr1', '648.dv1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [26461, 1728, 15552, 18576, 12384, 2592], 'label': '31104.fx.216.dy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1', 'old_label': '216.dy1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dy1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186248710
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bf1', '108.w1', '108.cb1', '108.fm1'], 'contains': ['432.ek1', '432.ek2', '432.eo1', '648.ds1', '648.dy1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [16057, 12384, 15552, 18576, 1728, 2592], 'label': '31104.fx.216.dz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bf1', 'old_label': '216.dz1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dz1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 186248711
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.p1', '72.bg1', '72.bh1', '72.bi1'], 'contains': ['432.eq1', '432.gc1', '432.hf1', '648.dz1', '648.ea1', '648.eb1', '864.gn1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [20737, 15552, 18648, 36, 12460, 16080], 'label': '31104.fx.216.ea1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ea1', 'old_label': '216.ea1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ea1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
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id: 186248712
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '18.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.n1'], 'contains': ['36.cd1', '36.ce1', '36.cy1', '54.bx1', '54.ce1', '72.fe1'], 'core': '648.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [5713, 15552, 22752, 2664, 6, 12096, 2592, 18576, 15628], 'label': '31104.fx.18.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bl1', 'old_label': '18.bl1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bl1', 'subgroup_fusion': None, 'weyl_group': '1728.12469'}
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id: 186248713
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.eb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.u1', '72.bg1', '72.bj1'], 'contains': ['432.bd1', '432.bg1', '432.bu1', '432.cg1', '432.er1', '432.fh1', '432.gn1', '648.dz1', '648.ec1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [20737, 22752, 21292, 36, 3096, 15552], 'label': '31104.fx.216.eb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.eb1', 'old_label': '216.eb1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.eb1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186248714
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ec1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.bg1', '72.bk1', '108.cl1'], 'contains': ['432.es1', '432.fi1', '432.go1', '648.ea1', '648.ec1', '864.gs1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1, 18144, 72, 36, 12940, 10368], 'label': '31104.fx.216.ec1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cl1', 'old_label': '216.ec1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ec1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186248715
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ed1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.v1', '72.bg1', '72.bl1'], 'contains': ['432.et1', '432.fj1', '432.gp1', '648.eb1', '648.ec1', '864.gt1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [20737, 15552, 18648, 36, 16080, 22752], 'label': '31104.fx.216.ed1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ed1', 'old_label': '216.ed1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ed1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186248716
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ee1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.w1', '72.bg1', '72.bl1', '72.bm1'], 'contains': ['432.eu1', '432.fk1', '432.gq1', '648.eb1', '648.ec1', '864.gu1'], 'core': '10368.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [1, 15552, 18648, 36, 16080, 10368], 'label': '31104.fx.216.ee1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ee1', 'old_label': '216.ee1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ee1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186248717
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ef1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.x1', '72.bi1', '72.bj1'], 'contains': ['432.be1', '432.bh1', '432.bv1', '432.ch1', '432.ev1', '432.fq1', '432.gt1', '648.dz1', '648.ee1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [20737, 2016, 10924, 36, 3096, 15552], 'label': '31104.fx.216.ef1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ef1', 'old_label': '216.ef1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ef1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186248718
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.eg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.y1', '72.bh1', '72.bj1', '72.bn1'], 'contains': ['432.bf1', '432.bi1', '432.bw1', '432.ci1', '432.ew1', '432.fr1', '432.gu1', '648.dz1', '648.ed1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [20737, 12384, 556, 36, 3096, 15552], 'label': '31104.fx.216.eg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.eg1', 'old_label': '216.eg1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.eg1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 186248719
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.eh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bh1', '72.bk1', '108.cm1'], 'contains': ['432.ex1', '432.fs1', '432.gv1', '648.ea1', '648.ed1', '864.gv1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [20737, 18144, 72, 36, 10924, 2016], 'label': '31104.fx.216.eh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cm1', 'old_label': '216.eh1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.eh1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186248720
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ei1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bi1', '72.bk1', '72.bo1', '108.cn1'], 'contains': ['432.ey1', '432.ft1', '432.gw1', '648.ea1', '648.ee1', '864.gw1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [20737, 18144, 72, 36, 556, 12384], 'label': '31104.fx.216.ei1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cn1', 'old_label': '216.ei1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ei1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186248721
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.z1', '72.bh1', '72.bl1'], 'contains': ['432.ez1', '432.fu1', '432.gx1', '648.eb1', '648.ed1', '864.gx1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [20737, 15552, 18648, 36, 16080, 12384], 'label': '31104.fx.216.ej1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ej1', 'old_label': '216.ej1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ej1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 186248722
{'ambient': '31104.fx', 'aut_centralizer_order': None, 'aut_label': '216.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.z1', '72.bi1', '72.bl1'], 'contains': ['432.fa1', '432.fv1', '432.gy1', '648.eb1', '648.ee1', '864.gx1'], 'core': '31104.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [20737, 18144, 72, 36, 16080, 12384], 'label': '31104.fx.216.ek1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ek1', 'old_label': '216.ek1', 'projective_image': '31104.fx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ek1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
